%0 Journal Article %J Int. Math. Res. Not. vol. 2008, Article ID rnn038 %D 2008 %T Noncommutative families of instantons %A Giovanni Landi %A Chiara Pagani %A Cesare Reina %A Walter van Suijlekom %X 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 $Sp_\\\\theta(2)$. %B Int. Math. Res. Not. vol. 2008, Article ID rnn038 %I Oxford University Press %G en_US %U http://hdl.handle.net/1963/3417 %1 918 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-01-12T09:40:47Z\\nNo. of bitstreams: 1\\n0710.0721v2.pdf: 290960 bytes, checksum: 7203f1e1dd34fd90d8d3201c7b813b44 (MD5) %R 10.1093/imrn/rnn038 %0 Journal Article %J Commun. Math. Phys. 259 (2005) 729-759 %D 2005 %T The Dirac operator on SU_q(2) %A Ludwik Dabrowski %A Giovanni Landi %A Andrzej Sitarz %A Walter van Suijlekom %A Joseph C. Varilly %X 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. %B Commun. Math. Phys. 259 (2005) 729-759 %I Springer %G en %U http://hdl.handle.net/1963/4425 %1 4175 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-04T08:01:47Z No. of bitstreams: 1 math_0411609v2.pdf: 293099 bytes, checksum: cfa2846ded2ecf161e83f4269b65e9b2 (MD5) %R 10.1007/s00220-005-1383-9 %0 Journal Article %J K-Theory 35 (2005) 375-394 %D 2005 %T The local index formula for SUq(2) %A Walter van Suijlekom %A Ludwik Dabrowski %A Giovanni Landi %A Andrzej Sitarz %A Joseph C. Varilly %X 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. %B K-Theory 35 (2005) 375-394 %G en_US %U http://hdl.handle.net/1963/1713 %1 2438 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-01-18T10:14:50Z\\nNo. of bitstreams: 1\\nmath.QA0501287.pdf: 189281 bytes, checksum: 75a780cbe958f6093e340102ad9bf176 (MD5) %R 10.1007/s10977-005-3116-4 %0 Journal Article %J Comm. Math. Phys. 260 (2005) 203-225 %D 2005 %T Principal fibrations from noncommutative spheres %A Giovanni Landi %A Walter van Suijlekom %X 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. %B Comm. Math. Phys. 260 (2005) 203-225 %G en_US %U http://hdl.handle.net/1963/2284 %1 1732 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-22T14:25:11Z\\nNo. of bitstreams: 1\\n0410077v3.pdf: 291352 bytes, checksum: 91d11a43e2221278d597a48ce274e4a5 (MD5) %R 10.1007/s00220-005-1377-7