Derivations of a family of quantum second Weyl algebras

Abstract

In view of a well-known theorem of Dixmier, its is natural to consider primitive quotients of Uq+(g) as quantum analogues of Weyl algebras. In this work, we study primitive quotients of Uq+(G2) and compute their Lie algebra of derivations. In particular, we show that, in some cases, all derivations are inner showing that the corresponding primitive quotients of Uq+(G2) should be considered as deformations of Weyl algebras.