Noncommutative geometry on central extension of U(u(2))

Abstract

In our previous publications, we have introduced analogs of partial derivatives on the reflection equation algebras, associated with Hecke symmetries. As a consequence, we get quantum partial derivatives on the enveloping algebras U(gl(N)). In the current paper, we consider the particular case N = 2 in detail and discuss the problem of a prolongation of these derivatives onto some central extension of the compact form U(u(2)) of the algebra U(gl(2)). Possible applications of this noncommutative geometry are discussed.