Equivariant quantizations of symmetric algebras

JOURNAL OF ALGEBRA

卷:322

Article

Zwicknagl, Sebastian

关键词: Quantum groups;    Poisson geometry;    Classical invariant theory;    Lie bialgebras;   

DOI  :  10.1016/j.jalgebra.2009.08.007

来源: Elsevier

【 摘 要 】

Let g be a Lie bialgebra and let V be a finite-dimensional g-module. We study deformations of the symmetric algebra of V which are equivariant with respect to an action of the quantized enveloping algebra U-h(g), resp. U-q(g). We investigate, in particular, such quantizations obtained from the quantization of certain Lie bialgebra structures on the semidirect product of g and V. We classify these structure in the important special case, when g is complex, simple, with quasitriangular Lie bialgebra structure and V is a simple g-module. We then introduce a more general notion, co-Poisson module algebras and their quantizations, to further address the problem and show that many known examples of quantized symmetric algebras can be described in this language. (C) 2009 Published by Elsevier Inc.

【 授权许可】

Free