Equivariant Quantizations of Symmetric Algebras

2008/10/12 by Sebastian Zwicknagl, Zwicknagl, Sebastian
Mathematics · #17B37 #17B63 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.0810.2130

openalex publication_date 2008/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 of g. In particular we investigate 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 more a 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.

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