Quantized function algebras at q=0: type A_n case

2022/03/28 by Manabendra Giri, Giri, Manabendra, Arup Kumar Pal +1 · 1 citation
Mathematics · #17B37 #20G42 #46L67 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2203.14665

openalex publication_date 2022/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define the notion of quantized function algebras at q=0 or crystallization of the q deformations of the type A_n compact Lie groups at the C^*-algebra level. The C^*-algebra A_n(0) is defined as a universal C^*-algebra given by a finite set of generators and relations. We obtain these relations by looking at the irreducible representations of the quantized function algebras for q>0 and taking limit as q→ 0+ after rescaling the generating elements appropriately. We then prove that in the n=2 case the irreducible representations A₂(0) are precisely the q→ 0+ limits of the irreducible representations of the C^*-algebras A₂(q).

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