Notes on the differential calculi on quantum linear groups

Abstract

This talk is devoted to the problem of constructing differential calculi on quantum linear groups. Based on the natural algebraic postulates, we examine the possible commutation relations for theGL q(N)- andSL q(N)-invariant differential forms and vector fields. It turns out that there exist several families of admissible commutation rules forGL q(N), but, in contrast, the commutation prescription forSL q(N) is unique.