Equivariant spectral triples on the quantum SU(2) group
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In this article, the authors characterized all equivariant odd spectral triples for the quantum SU(2) group acting on its L2-space and having a nontrivial Chern character.Abstract:
We characterize all equivariant odd spectral triples for the quantum SU(2) group acting on its L2-space and having a nontrivial Chern character. It is shown that the dimension of an equivariant spectral triple is at least three, and given any element of the K-homology group of SUq(2), there is an equivariant odd spectral triple of dimension 3 inducing that element. The method employed to get equivariant spectral triples in the quantum case is then used for classical SU(2), and we prove that for p<4, there does not exist any equivariant spectral triple with nontrivial K-homology class and dimension p acting on the L2-space.read more
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An Introduction to Noncommutative Geometry
TL;DR: In this paper, a course on non-commutative geometry from the non-computative point of view was presented at the 1997 Summer School on Non-Commutative Geometry and Applications at the European Mathematical Society (EMS) at Monsaraz and Lisboa, Portugal, September 1-10, 1997.
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CYCLIC COHOMOLOGY, QUANTUM GROUP SYMMETRIES AND THE LOCAL INDEX FORMULA FOR SU q (2)
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The spectral action for Moyal planes
Victor Gayral,Bruno Iochum +1 more
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References
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K-Theory for Operator Algebras
TL;DR: A survey of topological K-theory can be found in this paper, where the authors present a survey of applications to geometry and topology, including the Pimsner-Voiculescu exact sequence and Connes' Thorn isomorphism.
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Twisted SU (2) group. An example of a non-commutative differential calculus
TL;DR: In this paper, a C*-algebre A engendree par deux elements α et γ satisfaisant une relation de commutation simple dependante de ν is presented.
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The Künneth theorem and the universal coefficient theorem for Kasparov’s generalized $K$-functor
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Quantum deformation of lorentz group
TL;DR: In this article, a one parameter quantum deformation SμL(2,ℂ) of the double group SμU(2) is introduced and an analog of the Iwasawa decomposition is proved.