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Equivariant spectral triples on the quantum SU(2) group

Partha Sarathi Chakraborty·Arupkumar Pal
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Abstract

We characterize all equivariant odd spectral triples for the quantum SU(2) group acting on its L_2-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 SU_q(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 L_2-space.

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Partha Sarathi Chakraborty, Arupkumar Pal. 2002-10-03. Equivariant spectral triples on the quantum SU(2) group. https://arxiv.org/abs/math/0201004

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