Index theorems for noncommutative two-tori and Hochschild cohomology for quantum special linear groups

This paper covers three main topics. The first is addressing the question of interpolating between disparate index theorems on noncommutative two-tori. The second is to compute Hochschild cohomology for quantum special linear and special unitary groups. The third is producing an orthonormal basis for the vector space of matrix corepresentations for quantum special unitary groups.