Braided Symmetric Algebras of Simple U_q(sl₂)-Modules and Their Geometry

2010/09/15 by Sebastian Zwicknagl, Zwicknagl, Sebastian
Mathematics · #17B37 #81R60 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #msc:17B37 #msc:81R60

paper · pdf · doi:10.48550/arxiv.1009.2931

19 pages,relationship to non--commutative geometry expanded

openalex publication_date 2010/09/15 · arxiv created 2012/02/29 · arxiv updated 2012/03/01 · openalex created_date 2025/10/27 · openalex updated_date 2026/07/28

Abstract

In the present paper we prove decomposition formulae for the braided symmetric powers of simple modules over the quantized enveloping algebra U_q(sl₂); natural quantum analogues of the classical symmetric powers of a module over a complex semisimple Lie algebra. We show that their point modules form natural non-commutative curves and surfaces and conjecture that braided symmetric algebras give rise to an interesting non-commutative geometry, which can be viewed as a flat deformation of the geometry associated to their classical limits.

Citations

• Some Algebras Associated to Automorphisms of Elliptic Curves
• Noncommutative Projective Schemes

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