32 citations · 73 across the 34 of their papers we have counts for
35 papers
Monoidal structures arising from -algebras with applications to Hopf algebras
Gongxiang Liu, Zhengfang Wang, Mengdie Zhang
We give an explicit construction of monoidal structures on derived categories of right -modules over an -algebra equipped with a -structure. Given…
Exact sequences of rt-categories
Menggao Li, Gongxiang Liu
Our aim is to consider what the exact sequence for rt-categories is. For this, we introduce the notion of exact sequence of rt-categories, modeled on exact sequences of finite tens…
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…
Quotient Category of a Multiring Category
Zhenbang Zuo, Gongxiang Liu
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…
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…
The Grothendieck algebras of certain smash product semisimple Hopf algebras
Zhihua Wang, Gongxiang Liu, Libin Li
Let 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…
Higher Frobenius-Schur indicators for semisimple Hopf algebras in positive characteristic
Zhihua Wang, Gongxiang Liu, Libin Li
Let be a semisimple Hopf algebra over an algebraically closed field $\mathbbm{k}$ of characteristic $p>\dim_{\mathbbm{k}}(H)^{1/2}$. We show that the antipode of satisf…
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…
The Finite Duals of Affine Prime Regular Hopf Algebras of GK-Dimension One
Kangqiao Li, Gongxiang Liu
This paper is an attempt to construct a special kind of Hopf pairing . Specifically, and should be both affine…
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 combinatorial identity and the finite dual of infinite dihedral group algebra
Fan Ge, Gongxiang Liu
In this note, we find a combinatorial identity which is closely related to the multi-dimensional integral in the study of divisor functions. As an application, we determine…
Quasitriangular structures on the 8-dimensional Kac algebra K_8
Kun Zhou, Gongxiang Liu
In this note, we give a list of all non-isomorphic quasitriangular structures on the 8-dimension Kac algebra K_8.
On the Antipode of Hopf Algebras with the Dual Chevalley Property
Kangqiao Li, Gongxiang Liu
In this paper, we study the antipode of a finite-dimensional Hopf algebra with the dual Chevalley property and obtain an annihilation polynomial for its antipode . The annih…
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…
Classification of affine prime regular Hopf algebras of GK-dimension one
Jinyong Wu, Gongxiang Liu, Nanqing Ding
The classification of affine prime regular Hopf algebras of GK-dimension one is completed. As consequences, 1) we give a negative answer to an open question posed by Brown-Zhang an…
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…
On Braided Linear Gr-categories
Hua-Lin Huang, Gongxiang Liu, Yu Ye
We provide explicit and unified formulae for the normalized 3-cocycles on arbitrary finite abelian groups. As an application, we compute all the braided monoidal structures on line…
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 .