I will give examples of noncommutative selfcoverings, and describe how a spectral triple on the base space can be extended to a spectral triple on the inductive family of coverings, in such a way that the covering projections are locally isometric.I will show that such triples converge, in a suitable sense, to a semifinite spectral triple on the direct limit of the tower of coverings, which I call noncommutative solenoidal space.Some of the selfcoverings described are given by the inclusion of the fixed point algebra in a $C^*$algebra acted upon by a finite abelian group.In all the examples treated, the noncommutative solenoidal spaces have the same metric dimension and volume as the base space, while the pseudometric induced by the spectral triple does not produce the weak$^*$ topology on the state space.
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Spectral triples for noncommutative solenoidal spaces from selfcoverings
Research Group:
Prof.
Tommaso Isola
Institution:
Roma "Tor Vergata"
Location:
A136
Schedule:
Wednesday, June 22, 2016  16:00
Abstract:
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