32 citations · 73 across the 34 of their papers we have counts for
21 papers · 1 filter
On the Classification of Finite Quasi-Quantum Groups over Abelian Groups
Hua-Lin Huang, Gongxiang Liu, Yuping Yang +1
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 ov…
Hopf algebras with the dual Chevalley property of finite corepresentation type
Jing Yu, Kangqiao Li, Gongxiang Liu
Let be a finite-dimensional Hopf algebra over an algebraically closed field with the dual Chevalley property. We prove that is of finite corepresentation type if an…
Finite dimensional Nichols algebras over of Kashina
Miantao Liu, Gongxiang Liu, Kun Zhou
Let be the Hopf algebra of Kashina [J. Algebra, 232(2000),pp.617-663]. We give all simple Yetter-Drinfel'd modules over , then classify all finite-dimensi…
On the stable equivalences between finite tensor categories
Yuying Xu, Gongxiang Liu
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 induc…
Invariants from the Sweedler power maps on integrals
Zhihua Wang, Gongxiang Liu, Libin Li
For a finite-dimensional Hopf algebra with a nonzero left integral , we investigate a relationship between and , where and are respectively…
Quasitriangular Hopf algebras of dimension pq^2
Kun Zhou, Gongxiang Liu
Let p and q be distinct odd primes and assume k is an algebraically closed field of characteristic zero. We classify all quasitriangular Hopf algebras of dimension pq^2 over k, whi…
On the quasitriangular structures of abelian extensions of
Kun Zhou, Gongxiang Liu
The aim of this paper is to study quasitriangular structures on a class of semisimple Hopf algebras constructed through abelian extensions of for an abelian group . We pro…
A classification result on prime Hopf algebras of GK-dimension one
Gongxiang Liu
In this paper, we classify all prime Hopf algebras of GK-dimension one satisfying the following two conditions: 1) has a 1-dimensional representation of order PI.deg a…
Finite quasi-quantum groups of diagonal type
Hua-Lin Huang, Gongxiang Liu, Yuping Yang +1
The goal of the present paper is to classify an interesting class of elementary quasi-Hopf algebras, or equivalently, finite-dimensional pointed Majid algebras. By a Tannaka-Krein…
Finite quasi-quantum groups of rank two
Hua-Lin Huang, Gongxiang Liu, Yuping Yang +1
This is a contribution to the structure theory of finite pointed quasi-quantum groups. We classify all finite-dimensional connected graded pointed Majid algebras of rank two which…
Representations of the small quasi-quantum group
Gongxiang Liu, Fred Van Oystaeyen, Yinhuo Zhang
The quasi-Frobenius-Lusztig kernel associated with has been constructed in \cite{Liu}. In this paper we study the represe…
Graded elementary quasi-Hopf algebras of tame representation type
Hua-Lin Huang, Gongxiang Liu, Yu Ye
The class of graded elementary quasi-Hopf algebras of tame type is classified. Combining with our previous work [19], this completes the trichotomy for such class of algebras accor…
Quasi-Frobenius-Lusztig kernels for simple Lie algebras
Gongxiang Liu, Fred Van Oystaeyen, Yinhuo Zhang
In this paper, we construct the quasi-Frobenius-Lusztig kernel for any simple Lie algebra .
On Total Frobenius-Schur Indicators
Gongxiang Liu, Siu-Hung Ng
We define total Frobenius-Schur indicator for each object in a spherical fusion category as a certain canonical sum of its higher indicators. The total indicators are invariant…
The braided monoidal structures on a class of linear Gr-categories
Hua-Lin Huang, Gongxiang Liu, Yu Ye
A linear Gr-category is a category of finite-dimensional vector spaces graded by a finite group together with natural tensor product. We classify the braided monoidal structures of…
The quasi-Hopf analogue of
Gongxiang Liu
In [4], some quasi-Hopf algebras of dimension , which can be understood as the quasi-Hopf analogues of Taft algebras, are constructed. Moreover, the quasi-Hopf analogues of…
A Hochschild's 6-term exact sequence for restricted Lie superalgebras
Gongxiang Liu
In [5], Hochschild established a 6-term exact sequence for the cohomology of restricted Lie algebras. We generalize this result to restricted Lie superalgebras.
On coquasitriangular pointed Majid algebras
Hua-Lin Huang, Gongxiang Liu
We study coquasitriangular pointed Majid algebras via the quiver approaches. The class of Hopf quivers whose path coalgebras admit coquasitriangular Majid algebras is classified. T…
On quiver-theoretic description for quasitriangularity of Hopf algebras
Hua-Lin Huang, Gongxiang Liu
This paper is devoted to the study of the quasitriangularity of Hopf algebras via Hopf quiver approaches. We give a combinatorial description of the Hopf quivers whose path coalgeb…
Quivers, Quasi-Quantum Groups and Finite Tensor Categories
Hua-Lin Huang, Gongxiang Liu, Yu Ye
We study finite quasi-quantum groups in their quiver setting developed recently by the first author in arXiv:0902.1620 and arXiv:0903.1472. We obtain a classification of finite-dim…
On the Structure of Tame Graded Basic Hopf Algebras II
Hua-Lin Huang, Gongxiang Liu
In continuation of the article \cite{L} we classify all radically graded basic Hopf algebras of tame type over an algebraically closed field of characteristic 0.