A q-analogue of the dual space to the Lie algebras gl(2) and sl(2)

Abstract

For the Lie group GL(n), the linear Poisson bracket on the dual space gl(n)* to the Lie algebra gl(n) is quadratically deformed to make the coadjoint action of GL(n) into a Poisson action, for arbitrary quadratic Poisson Lie structure on GL(n). For the case n=2, these formulae are quantized for both quantum groups GLq(2) and SLq(2).