R-Matrix Poisson Algebras and Their Deformations

2007/06/03 by Sebastian Zwicknagl, Zwicknagl, Sebastian · 2 citations
Mathematics · #17B37 #17B63 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT #msc:17B37 #msc:17B63

paper · pdf · doi:10.48550/arxiv.0706.0351

50 pages

arxiv created 2007/06/03 · openalex publication_date 2007/06/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify in this paper Poisson structures on modules over semisimple Lie algebras arising from classical r-matrices. We then study their quantizations and the relation to classical invariant theory.

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• Group valued moment maps for even and odd simple G-modules
• Braided symmetric algebras and a first fundamental theorem of invariant theory for \rm U_q(G₂)

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