Twisted Homology of Quantum SL(2) - Part II

TL;DR

This paper completes the calculation of twisted cyclic homology for the quantum SL(2) coordinate ring, constructing a nontrivial cyclic 3-cocycle analogous to a volume form in noncommutative geometry.

Contribution

It finalizes the twisted cyclic homology computation for quantum SL(2) and introduces a nontrivial 3-cocycle with geometric significance.

Findings

Constructed a nontrivial cyclic 3-cocycle.

Identified a nontrivial class in Hochschild cohomology.

Established a noncommutative volume form analogue.

Abstract

We complete the calculation of the twisted cyclic homology of the quantised coordinate ring of SL(2) that we began in math.QA/0405249. In particular, a nontrivial cyclic 3-cocycle is constructed which also has a nontrivial class in Hochschild cohomology and thus should be viewed as a noncommutative geometry analogue of a volume form.