TY - RPRT
T1 - The Gysin Sequence for Quantum Lens Spaces
Y1 - 2014
A1 - Francesca Arici
A1 - Simon Brain
A1 - Giovanni Landi
AB - We define quantum lens spaces as `direct sums of line bundles' and exhibit them as `total spaces' of certain principal bundles over quantum projective spaces. For each of these quantum lens spaces we construct an analogue of the classical Gysin sequence in K-theory. We use the sequence to compute the K-theory of the quantum lens spaces, in particular to give explicit geometric representatives of their K-theory classes. These representatives are interpreted as `line bundles' over quantum lens spaces and generically define `torsion classes'. We work out explicit examples of these classes.
UR - http://hdl.handle.net/1963/7246
N1 - 27 pages
U1 - 7288
U2 - Mathematics
U4 - 1
ER -
TY - RPRT
T1 - Pimsner algebras and Gysin sequences from principal circle actions
Y1 - 2014
A1 - Francesca Arici
A1 - Jens Kaad
A1 - Giovanni Landi
AB - A self Morita equivalence over an algebra B, given by a B-bimodule E, is thought of as a line bundle over B. The corresponding Pimsner algebra O_E is then the total space algebra of a noncommutative principal circle bundle over B. A natural Gysin-like sequence relates the KK-theories of O_E and of B. Interesting examples come from O_E a quantum lens space over B a quantum weighted projective line (with arbitrary weights). The KK-theory of these spaces is explicitly computed and natural generators are exhibited.
UR - http://urania.sissa.it/xmlui/handle/1963/34461
N1 - The preprint is composed of 30 pages and recorded in PDF format. Was published in arXiv
U1 - 34631
U2 - Mathematics
U4 - 1
U5 - MAT/07
ER -
TY - JOUR
T1 - Moduli spaces of noncommutative instantons: gauging away noncommutative parameters
JF - Quarterly Journal of Mathematics (2012) 63 (1): 41-86
Y1 - 2012
A1 - Simon Brain
A1 - Giovanni Landi
AB - Using the theory of noncommutative geometry in a braided monoidal category, we improve upon a previous construction of noncommutative families of instantons of arbitrary charge on the deformed sphere S^4_\\\\theta. We formulate a notion of noncommutative parameter spaces for families of instantons and we explore what it means for such families to be gauge equivalent, as well as showing how to remove gauge parameters using a noncommutative quotient construction. Although the parameter spaces are a priori noncommutative, we show that one may always recover a classical parameter space by making an appropriate choice of gauge transformation.
PB - Oxford University Press
UR - http://hdl.handle.net/1963/3777
U1 - 548
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - RPRT
T1 - Families of Monads and Instantons from a Noncommutative ADHM Construction
Y1 - 2009
A1 - Simon Brain
A1 - Giovanni Landi
AB - We give a \\\\theta-deformed version of the ADHM construction of SU(2) instantons with arbitrary topological charge on the sphere S^4. Classically the instanton gauge fields are constructed from suitable monad data; we show that in the deformed case the set of monads is itself a noncommutative space. We use these monads to construct noncommutative `families\\\' of SU(2) instantons on the deformed sphere S^4_\\\\theta. We also compute the topological charge of each of the families. Finally we discuss what it means for such families to be gauge equivalent.
UR - http://hdl.handle.net/1963/3478
U1 - 786
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - Gauged Laplacians on quantum Hopf bundles
JF - Comm. Math. Phys. 287 (2009) 179-209
Y1 - 2009
A1 - Giovanni Landi
A1 - Cesare Reina
A1 - Alessandro Zampini
AB - We study gauged Laplacian operators on line bundles on a quantum 2-dimensional sphere. Symmetry under the (co)-action of a quantum group allows for their complete diagonalization. These operators describe `excitations moving on the quantum sphere\\\' in the field of a magnetic monopole. The energies are not invariant under the exchange monopole/antimonopole, that is under inverting the direction of the magnetic field. There are potential applications to models of quantum Hall effect.
PB - Springer
UR - http://hdl.handle.net/1963/3540
U1 - 1161
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - The Isospectral Dirac Operator on the 4-dimensional Orthogonal Quantum Sphere
JF - Comm. Math. Phys. 279 (2008) 77-116
Y1 - 2008
A1 - Francesco D\'Andrea
A1 - Ludwik Dabrowski
A1 - Giovanni Landi
AB - Equivariance under the action of Uq(so(5)) is used to compute the left regular and (chiral) spinorial representations of the algebra of the quantum Euclidean 4-sphere S^4_q. These representations are the constituents of a spectral triple on this sphere with a Dirac operator which is isospectral to the canonical one of the spin structure of the round undeformed four-sphere and which gives metric dimension four for the noncommutative geometry. Non-triviality of the geometry is proved by pairing the associated Fredholm module with an `instanton\\\' projection. A real structure which satisfies all required properties modulo a suitable ideal of `infinitesimals\\\' is also introduced.
UR - http://hdl.handle.net/1963/2567
U1 - 1553
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - Noncommutative families of instantons
JF - Int. Math. Res. Not. vol. 2008, Article ID rnn038
Y1 - 2008
A1 - Giovanni Landi
A1 - Chiara Pagani
A1 - Cesare Reina
A1 - Walter D. van Suijlekom
AB - We construct $\\\\theta$-deformations of the classical groups SL(2,H) and Sp(2). Coacting on the basic instanton on a noncommutative four-sphere $S^4_\\\\theta$, we construct a noncommutative family of instantons of charge 1. The family is parametrized by the quantum quotient of $SL_\\\\theta(2,H)$ by $Sp_\\\\theta(2)$.
PB - Oxford University Press
UR - http://hdl.handle.net/1963/3417
U1 - 918
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - The Noncommutative Geometry of the Quantum Projective Plane
JF - Rev. Math. Phys. 20 (2008) 979-1006
Y1 - 2008
A1 - Francesco D\'Andrea
A1 - Ludwik Dabrowski
A1 - Giovanni Landi
AB - We study the spectral geometry of the quantum projective plane CP^2_q. In particular, we construct a Dirac operator which gives a 0^+ summable triple, equivariant under U_q(su(3)).
UR - http://hdl.handle.net/1963/2548
U1 - 1571
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - Dirac operators on all Podles quantum spheres
JF - J. Noncomm. Geom. 1 (2007) 213-239
Y1 - 2007
A1 - Francesco D\'Andrea
A1 - Ludwik Dabrowski
A1 - Giovanni Landi
A1 - Elmar Wagner
AB - We construct spectral triples on all Podles quantum spheres. These noncommutative geometries are equivariant for a left action of $U_q(su(2))$ and are regular, even and of metric dimension 2. They are all isospectral to the undeformed round geometry of the 2-sphere. There is also an equivariant real structure for which both the commutant property and the first order condition for the Dirac operators are valid up to infinitesimals of arbitrary order.
UR - http://hdl.handle.net/1963/2177
U1 - 2067
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - A Hopf bundle over a quantum four-sphere from the symplectic group
JF - Commun. Math. Phys. 263 (2006) 65-88
Y1 - 2006
A1 - Giovanni Landi
A1 - Chiara Pagani
A1 - Cesare Reina
AB - We construct a quantum version of the SU(2) Hopf bundle $S^7 \\\\to S^4$. The quantum sphere $S^7_q$ arises from the symplectic group $Sp_q(2)$ and a quantum 4-sphere $S^4_q$ is obtained via a suitable self-adjoint idempotent $p$ whose entries generate the algebra $A(S^4_q)$ of polynomial functions over it. This projection determines a deformation of an (anti-)instanton bundle over the classical sphere $S^4$. We compute the fundamental $K$-homology class of $S^4_q$ and pair it with the class of $p$ in the $K$-theory getting the value -1 for the topological charge. There is a right coaction of $SU_q(2)$ on $S^7_q$ such that the algebra $A(S^7_q)$ is a non trivial quantum principal bundle over $A(S^4_q)$ with structure quantum group $A(SU_q(2))$.
UR - http://hdl.handle.net/1963/2179
U1 - 2065
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - The Dirac operator on SU_q(2)
JF - Commun. Math. Phys. 259 (2005) 729-759
Y1 - 2005
A1 - Ludwik Dabrowski
A1 - Giovanni Landi
A1 - Andrzej Sitarz
A1 - Walter DaniÃ«l Van Suijlekom
A1 - Joseph C. Varilly
AB - We construct a 3^+ summable spectral triple (A(SU_q(2)),H,D) over the quantum group SU_q(2) which is equivariant with respect to a left and a right action of U_q(su(2)). The geometry is isospectral to the classical case since the spectrum of the operator D is the same as that of the usual Dirac operator on the 3-dimensional round sphere. The presence of an equivariant real structure J demands a modification in the axiomatic framework of spectral geometry, whereby the commutant and first-order properties need be satisfied only modulo infinitesimals of arbitrary high order.
PB - Springer
UR - http://hdl.handle.net/1963/4425
N1 - v2: minor changes
U1 - 4175
U2 - Mathematics
U3 - Mathematical Physics
U4 - -1
ER -
TY - JOUR
T1 - The local index formula for SUq(2)
JF - K-Theory 35 (2005) 375-394
Y1 - 2005
A1 - Walter van Suijlekom
A1 - Ludwik Dabrowski
A1 - Giovanni Landi
A1 - Andrzej Sitarz
A1 - Joseph C. Varilly
AB - We discuss the local index formula of Connes-Moscovici for the isospectral noncommutative geometry that we have recently constructed on quantum SU(2). We work out the cosphere bundle and the dimension spectrum as well as the local cyclic cocycles yielding the index formula.
UR - http://hdl.handle.net/1963/1713
U1 - 2438
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - Principal fibrations from noncommutative spheres
JF - Comm. Math. Phys. 260 (2005) 203-225
Y1 - 2005
A1 - Giovanni Landi
A1 - Walter van Suijlekom
AB - We construct noncommutative principal fibrations S_\\\\theta^7 \\\\to S_\\\\theta^4 which are deformations of the classical SU(2) Hopf fibration over the four sphere. We realize the noncommutative vector bundles associated to the irreducible representations of SU(2) as modules of coequivariant maps and construct corresponding projections. The index of Dirac operators with coefficients in the associated bundles is computed with the Connes-Moscovici local index formula. The algebra inclusion $A(S_\\\\theta^4) \\\\into A(S_\\\\theta^7)$ is an example of a not trivial quantum principal bundle.
UR - http://hdl.handle.net/1963/2284
U1 - 1732
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - The spectral geometry of the equatorial Podles sphere
JF - C. R. Math. 340 (2005) 819-822
Y1 - 2005
A1 - Ludwik Dabrowski
A1 - Giovanni Landi
A1 - Mario Paschke
A1 - Andrzej Sitarz
AB - We propose a slight modification of the properties of a spectral geometry a la Connes, which allows for some of the algebraic relations to be satisfied only modulo compact operators. On the equatorial Podles sphere we construct suq2-equivariant Dirac operator and real structure which satisfy these modified properties.
UR - http://hdl.handle.net/1963/2275
U1 - 1972
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - Fredholm modules for quantum euclidean spheres
JF - J. Geom. Phys. 49 (2004) 272-293
Y1 - 2004
A1 - Eli Hawkins
A1 - Giovanni Landi
AB - The quantum Euclidean spheres, $S_q^{N-1}$, are (noncommutative) homogeneous spaces of quantum orthogonal groups, $\\\\SO_q(N)$. The *-algebra $A(S^{N-1}_q)$ of polynomial functions on each of these is given by generators and relations which can be expressed in terms of a self-adjoint, unipotent matrix. We explicitly construct complete sets of generators for the K-theory (by nontrivial self-adjoint idempotents and unitaries) and the K-homology (by nontrivial Fredholm modules) of the spheres $S_q^{N-1}$. We also construct the corresponding Chern characters in cyclic homology and cohomology and compute the pairing of K-theory with K-homology. On odd spheres (i. e., for N even) we exhibit unbounded Fredholm modules by means of a natural unbounded operator D which, while failing to have compact resolvent, has bounded commutators with all elements in the algebra $A(S^{N-1}_q)$.
PB - SISSA Library
UR - http://hdl.handle.net/1963/1636
U1 - 2482
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - Non-linear sigma-models in noncommutative geometry: fields with values in finite spaces
JF - Mod. Phys. Lett. A 18 (2003) 2371-2379
Y1 - 2003
A1 - Ludwik Dabrowski
A1 - Thomas Krajewski
A1 - Giovanni Landi
AB - We study sigma-models on noncommutative spaces, notably on noncommutative tori. We construct instanton solutions carrying a nontrivial topological charge q and satisfying a Belavin-Polyakov bound. The moduli space of these instantons is conjectured to consists of an ordinary torus endowed with a complex structure times a projective space $CP^{q-1}$.
PB - World Scientific
UR - http://hdl.handle.net/1963/3215
U1 - 1086
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - Instanton algebras and quantum 4-spheres
JF - Differential Geom. Appl. 16 (2002) 277-284
Y1 - 2002
A1 - Ludwik Dabrowski
A1 - Giovanni Landi
AB - We study some generalized instanton algebras which are required to describe `instantonic complex rank 2 bundles\\\'. The spaces on which the bundles are defined are not prescribed from the beginning but rather are obtained from some natural requirements on the instantons. They turn out to be quantum 4-spheres $S^4_q$, with $q\\\\in\\\\IC$, and the instantons are described by self-adjoint idempotents e. We shall also clarify some issues related to the vanishing of the first Chern-Connes class $ch_1(e)$ and on the use of the second Chern-Connes class $ch_2(e)$ as a volume form.
PB - Elsevier
UR - http://hdl.handle.net/1963/3134
U1 - 1199
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - Instantons on the Quantum 4-Spheres S^4_q
JF - Comm. Math. Phys. 221 (2001) 161-168
Y1 - 2001
A1 - Ludwik Dabrowski
A1 - Giovanni Landi
A1 - Tetsuya Masuda
AB - We introduce noncommutative algebras $A_q$ of quantum 4-spheres $S^4_q$, with $q\\\\in\\\\IR$, defined via a suspension of the quantum group $SU_q(2)$, and a quantum instanton bundle described by a selfadjoint idempotent $e\\\\in \\\\Mat_4(A_q)$, $e^2=e=e^*$. Contrary to what happens for the classical case or for the noncommutative instanton constructed in Connes-Landi, the first Chern-Connes class $ch_1(e)$ does not vanish thus signaling a dimension drop. The second Chern-Connes class $ch_2(e)$ does not vanish as well and the couple $(ch_1(e), ch_2(e))$ defines a cycle in the $(b,B)$ bicomplex of cyclic homology.
PB - Springer
UR - http://hdl.handle.net/1963/3135
U1 - 1198
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - Some Properties of Non-linear sigma-Models in Noncommutative Geometry
JF - Int. J. Mod. Phys. B 14 (2000) 2367-2382
Y1 - 2000
A1 - Ludwik Dabrowski
A1 - Thomas Krajewski
A1 - Giovanni Landi
AB - We introduce non-linear $\\\\sigma$-models in the framework of noncommutative geometry with special emphasis on models defined on the noncommutative torus. We choose as target spaces the two point space and the circle and illustrate some characteristic features of the corresponding $\\\\sigma$-models. In particular we construct a $\\\\sigma$-model instanton with topological charge equal to 1. We also define and investigate some properties of a noncommutative analogue of the Wess-Zumino-Witten model.
PB - SISSA Library
UR - http://hdl.handle.net/1963/1373
U1 - 3082
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - Algebraic differential calculus for gauge theories
JF - Nuclear Phys. B. Proc. Suppl. 18A (1990), 171
Y1 - 1990
A1 - Giovanni Landi
A1 - Giuseppe Marmo
PB - SISSA Library
UR - http://hdl.handle.net/1963/891
U1 - 2900
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - Chern-Simons forms on principal superfiber bundles
JF - J.Math.Phys.31:45,1990
Y1 - 1990
A1 - Giovanni Landi
A1 - Claudio Bartocci
A1 - Ugo Bruzzo
AB - A graded Weil homomorphism is defined for principal superfiber bundles and the related transgression (or Chern-Simons) forms are introduced. As an example of the application of these concepts, a ``superextension\\\'\\\' of the Dirac monopole is discussed.
PB - SISSA Library
UR - http://hdl.handle.net/1963/590
U1 - 3314
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - Algebraic reduction of the \\\'t Hooft-Polyakov monopole to the Dirac monopole.
JF - Phys. Lett. B 201 (1988), no. 1, 101-104.
Y1 - 1988
A1 - Giovanni Landi
A1 - Giuseppe Marmo
PB - SISSA Library
UR - http://hdl.handle.net/1963/578
U1 - 3326
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - THES
T1 - An Algebraic Setting for Gauge Theories
Y1 - 1988
A1 - Giovanni Landi
PB - SISSA
UR - http://hdl.handle.net/1963/5828
U1 - 5677
U2 - Mathematics
U3 - Mathematical Physics
U4 - -1
ER -
TY - JOUR
T1 - Einstein algebras and the algebraic Kaluza-Klein monopole.
JF - Phys. Lett. B 210 (1988), no. 1-2, 68--72.
Y1 - 1988
A1 - Giovanni Landi
A1 - Giuseppe Marmo
PB - SISSA Library
UR - http://hdl.handle.net/1963/603
U1 - 3301
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - Extensions of Lie superalgebras and supersymmetric Abelian gauge fields.
JF - Phys. Lett. B 193 (1987), no. 1, 61-66.
Y1 - 1987
A1 - Giovanni Landi
A1 - Giuseppe Marmo
PB - SISSA Library
UR - http://hdl.handle.net/1963/507
U1 - 3397
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - Graded Chern-Simons terms
JF - Phys. Lett. B 192 (1987), no. 1-2, 81-88.
Y1 - 1987
A1 - Giovanni Landi
A1 - Giuseppe Marmo
PB - SISSA Library
UR - http://hdl.handle.net/1963/508
U1 - 3396
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - Lie algebra extensions and abelian monopoles.
JF - Phys. Lett. B 195 (1987), no. 3, 429-434
Y1 - 1987
A1 - Giovanni Landi
A1 - Giuseppe Marmo
PB - SISSA Library
UR - http://hdl.handle.net/1963/506
U1 - 3398
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - The natural spinor connection on $S\\\\sb 8$ is a gauge field
JF - Lett. Math. Phys. 11 (1986), no. 2, 171-175
Y1 - 1986
A1 - Giovanni Landi
PB - SISSA Library
UR - http://hdl.handle.net/1963/448
U1 - 3455
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - Flat connections for Lax hierarchies on coadjoint orbits
JF - Phys. Lett. A 108 (1985), no. 7, 311--314.
Y1 - 1985
A1 - Sergio De Filippo
A1 - Giovanni Landi
PB - SISSA Library
UR - http://hdl.handle.net/1963/383
U1 - 3584
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - Flat connections for Lax hierarchies on coadjoint orbits
JF - Phys. Lett. A 108 (1985), no. 7, 311-314
Y1 - 1985
A1 - Giovanni Landi
A1 - Sergio De Filippo
PB - SISSA Library
UR - http://hdl.handle.net/1963/460
U1 - 3443
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - Maximal acceleration and Sakharov\\\'s limiting temperature
JF - Lett. Nuovo Cim. 42 (1985) 70-72
Y1 - 1985
A1 - Eduardo R. Caianiello
A1 - Giovanni Landi
AB - It is shown that Sakharov\\\'s maximal temperature, derived by him from astrophysical considerations, is a straightforward consequence of the maximal acceleration introduced by us in previous works.
PB - SocietÃ Italiana di Fisica
UR - http://hdl.handle.net/1963/372
U1 - 3595
U2 - Physics
U3 - Elementary Particle Theory
ER -