On product type actions of G_q

2013/02/10 by Reiji Tomatsu, Tomatsu, Reiji
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #math.OA

paper · pdf · doi:10.48550/arxiv.1302.2335

39 pages, minor corrections, Section 3.1 is added and Section 5 is rewitten

openalex publication_date 2013/02/10 · arxiv created 2013/03/31 · arxiv updated 2013/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We will study a faithful product type action of G_q that is the q-deformation of a connected semisimple compact Lie group G, and prove that such an action is induced from a minimal action of the maximal torus T of G_q. This enables us to classify product type actions of SU_q(2) up to conjugacy. We also compute the intrinsic group of G_q,Ω, the 2-cocycle deformation of G_q that is naturally associated with the quantum flag manifold T\backslash G_q.

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