mathfrakR-matrix for quantum superalgebra mathfraksl(2|1) at\n roots of unity and its application to centralizer algebras

2019/09/25 by A. Mazurenko, Mazurenko, Alexander, Vladimir Stukopin +1
Computer Science · Mathematics · Physics and Astronomy · #16W30 (Secondary) #16W35 (Primary) 16W55 #17B37 #81R50 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Matrix Theory and Algorithms #Nonlinear Waves and Solitons #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1909.11613

openalex publication_date 2019/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider fundamental facts from the theory of Hopf superalgebras. We use\nthem to construct the quantum double of the quantum superalgebra sl(2|1) at\nroots of unity. Thus we obtain a multiplicative formula for universal\nR-matrix. Next we construct an R-matrix to investigate parametrized family\nof centralizer algebras. We give multiplication laws in particular case and\ndescribe a structure of such algebras in the general case.\n

Related

• A universal R-matrix for the quantization of the Lie superalgebra D(2,1,x) and an associated link invariant
• The R-matrix of the symplecto-orthogonal quantum superalgebra U_q(spo(2n|2m)) in the vector representation
• Basic monodromy operator for quantum superalgebra
• Universal R-matrix for esoteric quantum group
• Representations at a Root of Unity of q-Oscillators and Quantum Kac-Moody algebras