Characterization of spectral triples: A combinatorial approach

Details Characterization of spectral triples: A combinatorial approach Characterization of spectral triples: A combinatorial approach

2003-05-12

arxiv.org/abs/math/0305157v3

Mathematics

Operator Algebras

v3: partly rewritten; the equivariant case has now been taken out and would be treated in a separate paper. v2: few typos corr

Scientific paper

We describe a general technique to study Dirac operators on noncommutative spaces under some additional assumptions. The main idea is to capture the compact resolvent condition in a combinatorial set up. Using this, we then prove that for a certain class of representations of the C^*-algebra C(SU_q(\ell+1)), any Dirac operator that diagonalises with respect to the natural basis of the underlying Hilbert space must have trivial sign.

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