On Gauge Equivalence of Twisted Quantum Doubles

2024/08/18 by Li, Bowen, Liu, Gongxiang · 1 citation
#16T05 #17B37 #18M20 #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2408.09353

Abstract

We study the quantum double of a finite abelian group G twisted by a 3-cocycle and give a sufficient condition when such a twisted quantum double will be gauge equivalent to a ordinary quantum double of a finite group. Moreover, we will determine when a twisted quantum double of a cyclic group is genuine. As an application, we contribute to the classification of coradically graded finite-dimensional pointed coquasi-Hopf algebras over abelian groups. As a byproduct, we show that the Nichols algebras B(M₁⊕ M₂ ⊕ M₃) are infinite-dimensional where M₁,M₂,M₃ are three different simple Yetter-Drinfeld modules of D₈.

Cited by

• Reflection of Nichols Algebras over Coquasi-Hopf Algebras

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