A class of semisimple Hopf algebras acting on quantum polynomial\n algebras

2017/10/07 by Deividi Pansera, Pansera, Deividi · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1710.02729

openalex publication_date 2017/10/07 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

We construct a class of non-commutative, non-cocommutative, semisimple Hopf\nalgebras of dimension 2n² and present conditions to define an inner faithful\naction of these Hopf algebras on quantum polynomial algebras, providing, in\nthis way, more examples of semisimple Hopf actions which do not factor through\ngroup actions. Also, under certain condition, we classify the inner faithful\nHopf actions of the Kac-Paljutkin Hopf algebra of dimension 8, H₈, on the\nquantum plane.\n

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