Presentations for small reflection equation algebras of type A

2024/12/20 by Cooke, Juliet, Robert Laugwitz, Laugwitz, Robert
Mathematics · Physics and Astronomy · #17B37 (Primary) 16T05 #18M05 #18M15 (Secondary) #Advanced Topics in Algebra #Category Theory (math.CT) #FOS: Mathematics #Nonlinear Waves and Solitons #Numerical methods for differential equations #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2412.16004

openalex publication_date 2024/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give presentations, in terms of the generators and relations, for the reflection equation algebras of type GL_n and SL_n, i.e., the covariantized algebras of the dual Hopf algebras of the small quantum groups of \mathfrakgl_n and \mathfraksl_n. Our presentations display these algebras as quotients of the infinite-dimensional reflection equation algebras of types GL_n and SL_n by identifying additional relations that correspond to twisting the nilpotency and unipotency relations of the finite-dimensional quantum function algebras. The presentations are valid for appropriately defined integral forms of these algebras.

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