q-index on braided non-commutative spheres

To some Yang-Baxter braidings of Hecke type we assign algebras called braided non-commutative spheres. For any such algebra, we introduce and compute a q-analog of the standard pairing Ind : K-0(A) x K-0(A) -> Z called a non-commutative index. Unlike the standard non-commutative index, our q-analog is based on the so-called categorical trace specific for a braided category in which the algebra in question is represented. (c) 2004 Published by Elsevier B.V.