Zobrazeno 1 - 10
of 139
pro vyhledávání: '"Liu, Gongxiang"'
Autor:
Li, Bowen, Liu, Gongxiang
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 result, we prove that all coradically graded pointed finite tensor ca
Externí odkaz:
http://arxiv.org/abs/2410.09549
Autor:
Yu, Jing, Liu, Gongxiang
We try to classify Hopf algebras with the dual Chevalley property of discrete corepresentation type over an algebraically closed field $\Bbb{k}$ with characteristic 0. For such Hopf algebra $H$, we characterize the link quiver of $H$ and determine th
Externí odkaz:
http://arxiv.org/abs/2409.20292
Autor:
Li, Bowen, Liu, Gongxiang
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
Externí odkaz:
http://arxiv.org/abs/2408.09353
Autor:
Yu, Jing, Liu, Gongxiang
Let $\Bbbk$ be an algebraically closed field of characteristic 0 and $H$ a finite-dimensional Hopf algebra over $\Bbbk$ with the dual Chevalley property. In this paper, we show that $\operatorname{gr}^c(H)$ is of tame corepresentation type if and onl
Externí odkaz:
http://arxiv.org/abs/2407.21389
Autor:
Zuo, Zhenbang, Liu, Gongxiang
The aim of this paper is to introduce a tensor structure for the Serre quotient category of an abelian monoidal category with biexact tensor product to make the canonical functor a monoidal functor. In this tensor product, the Serre quotient category
Externí odkaz:
http://arxiv.org/abs/2403.06244
Using a variety of methods developed in the theory of finite-dimensional quasi-Hopf algebras, we classify all finite-dimensional coradically graded pointed coquasi-Hopf algebras over abelian groups. As a consequence, we partially confirm the generati
Externí odkaz:
http://arxiv.org/abs/2403.04455
Let $H$ be a finite-dimensional Hopf algebra over an algebraically closed field $\Bbbk$ with the dual Chevalley property. We prove that $H$ is of finite corepresentation type if and only if it is coNakayama, if and only if the link quiver $\mathrm{Q}
Externí odkaz:
http://arxiv.org/abs/2308.09553
Let $H$ be the Hopf algebra $H_{c: \sigma_{0}}$ of Kashina [J. Algebra, 232(2000),pp.617-663]. We give all simple Yetter-Drinfel'd modules $V$ over $H$, then classify all finite-dimensional Nichols algebras of $V$. The finite dimensional Nichols alge
Externí odkaz:
http://arxiv.org/abs/2207.11863
Autor:
Xu, Yuying, Liu, Gongxiang
We aim to study Morita theory for tensor triangulated categories. For two finite tensor categories having no projective simple objects, we prove that their stable equivalence induced by an exact $\Bbbk$-linear monoidal functor can be lifted to a tens
Externí odkaz:
http://arxiv.org/abs/2203.10549
Let $H$ be a semisimple Hopf algebra over an algebraically closed field $\mathbbm{k}$ of characteristic $p>\dim_{\mathbbm{k}}(H)^{1/2}$ and $p\nmid 2\dim_{\mathbbm{k}}(H)$. In this paper, we consider the smash product semisimple Hopf algebra $H\#\mat
Externí odkaz:
http://arxiv.org/abs/2202.06302