6 papers · 1 filter
Classification of finite-dimensional Nichols algebras of rank two in twisted Yetter--Drinfeld categories
Bowen Li
Let \(G\) be a finite non-abelian group, let \(Φ\in Z^3(G,\mathbb C^\times)\) be normalized, and let \(V,W\) be finite-dimensional simple objects of \({}_G^G\mathcal{YD}^Φ\). We cl…
On the Cartan Graphs of Nichols Algebras over Coquasi-Hopf Algebras
Bowen Li
Over an algebraically closed field of characteristic zero, let be a coquasi-Hopf algebra with bijective antipode, and let be a tuple of finite-dimensional simple Yetter--Dr…
Reflection Theory of Nichols Algebras over Coquasi-Hopf Algebras with Bijective Antipode
Bowen Li, Gongxiang Liu
We investigate the reflection theory of Nichols algebras over arbitrary coquasi-Hopf algebras with bijective antipode, generalizing previous results restricted to the pointed cosem…
Reflection of Nichols Algebras over Coquasi-Hopf Algebras
Bowen Li, Gongxiang Liu
This paper extends the foundational reflection theory of Nichols algebras to the setting of some certain coquasi-Hopf algebras. Our primary motivation arises from the classificatio…
Cohomology of Pointed Finite Tensor Categories
Bowen Li, Gongxiang Liu
We consider the finite generation property for cohomology algebra of pointed finite tensor categories via de-equivariantization and exact sequence of finite tensor categories. As a…
On Gauge Equivalence of Twisted Quantum Doubles
Bowen Li, Gongxiang Liu
We study the quantum double of a finite abelian group twisted by a -cocycle and give a sufficient condition when such a twisted quantum double will be gauge equivalent to a…