# Deformations of Symmetric Module-Algebras

SPEAKER: Sebastian Zwicknagl

TITLE: Deformations of Symmetric Module-Algebras

ABSTRACT In this talk I will classify all modules $V$ over a complex simple Lie algebra $g$ , whose symmetric algebra can be deformed (flatly) into a module algebra $S_q(V)$ over the corresponding quantized enveloping algebra. I will define geometrically decomposable modules over Lie algebras, as introduced by Howe, and explain some of their properties. I will sketch how to prove that, unless the Lie algebra is $g=sp(2n)$, the algebra $S(V)$ can be deformed as indicated above, if and only if $V$ is geometrically decomposable. Finally, I will construct $S_q(V)$ for the simple geometrically decomposable modules.