Quantum groups, q-Boson algebras and quantized Weyl algebras

Abstract

We give a unified construction of quantum groups, q-Boson algebras and quantized Weyl algebras and an action of quantum groups on quantized Weyl algebras. This enables us to give a conceptual proof of the semi-simplicity of the category $\mathcal{O}(B_q)$ introduced by T.Nakashima and the classification of all simple objects in it.

18 pages, version to appear

References in corpus (1)

• Heisenberg double H(B^*) as a braided commutative Yetter-Drinfeld module algebra over the Drinfeld double

Cited by in corpus (1)

• On defining ideals and differential algebras of Nichols algebras