Characterization of spectral triples: A combinatorial approach
Operator Algebras
2007-05-23 v3 Combinatorics
Quantum Algebra
Abstract
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.
Keywords
Cite
@article{arxiv.math/0305157,
title = {Characterization of spectral triples: A combinatorial approach},
author = {Partha Sarathi Chakraborty and Arupkumar Pal},
journal= {arXiv preprint arXiv:math/0305157},
year = {2007}
}
Comments
v3: partly rewritten; the equivariant case has now been taken out and would be treated in a separate paper. v2: few typos corrected. LaTeX2e, uses xy-pic and eepic