Hui-xiang Chen

activity

20042026

most citedThe Green Ring of Drinfeld Double

D (H_{4})

20 citations · 35 across the 22 of their papers we have counts for

collaborators

24 papers

math.QA2026

The quantum double of the restricted quantum group $u_{q} (s l_{2})$

Hua Sun, Yijie Shen, Xiaoming Li +1

In this paper, we construct the quantum double $D (u_{q} (s l_{2}))$ of the restricted quantum group $u_{q} (s l_{2})$ . We describe…

math.QA2025

The Projective Class Rings of Drinfeld doubles of pointed rank one Hopf algebras

Hua Sun, Hui-Xiang Chen, Libin Li +1

Let $k$ be an algebraically closed field of characteristic $0$ . In this paper, we study the Grothendieck ring $G_{0} (D (H_{D}))$ and the projective class ring $r_p(D(H_\ma…

math.QA2025

Representations of the Drinfeld doubles of Pointed rank one Hopf algebras

Hua Sun, Huixiang Chen, Yinhuo Zhang

In this paper, we investigate the representations of the Drinfeld doubles $D (H_{D})$ of pointed rank one Hopf algebras $H_{D}$ over an algebraically closed fiel…

math.CT2023

Notes on semisimple tensor categories of rank two

Hua Sun, Hui-Xiang Chen, Yinhuo Zhang

In this paper, we show that there are infinitely many semisimple tensor (or monoidal) categories of rank two over an algebraically closed field $F$ .

math.QA2023★ 1 cited

Representations of the small quasi-quantum group

Hua Sun, Hui-Xiang Chen, Yinhuo Zhang

In this paper, we study the representation theory of the small quantum group $U_{q}$ and the small quasi-quantum group $U_{q}$ , where $q$ is a primitive $n$ -th r…

math.QA2023

Representations of Drinfeld Doubles of Radford Hopf algebras

Hua Sun, Hui-Xiang Chen

In this article, we investigate the representations of the Drinfeld doubles $D (R_{mn} (q))$ of the Radford Hopf algebras $R_{mn} (q)$ over an algebraically closed field $k$ , wher…

math.RA2021

Representations of Hopf-Ore extensions of group algebras

Hua Sun, Hui-Xiang Chen, Yinhuo Zhang

In this paper, we study the representations of the Hopf-Ore extensions $k G (χ^{- 1}, a, 0)$ of group algebra $k G$ , where $k$ is an algebraically closed field. We classify all finite…

math.RA2020

Examples of non-semisimple Hopf algebra actions on Artin-Schelter regular algebras

Hui-Xiang Chen, Ding-Guo Wang, James J. Zhang

Let $k$ be a base field of characteristic $p > 0$ and let $U$ be the restricted enveloping algebra of a 2-dimensional nonabelian restricted Lie algebra. We classify all inner-fai…

math.RA2020

Dorroh extensions of algebras and coalgebras, II

Lan You, Hui-Xiang Chen

In this paper, we study Dorroh extensions of bialgebras and Hopf algebras. Let $(H, I)$ be both a Dorroh pair of algebras and a Dorroh pair of coalgebras. We give necessary and suff…

math.RA2020

Dorroh extensions of algebras and coalgebras, I

Lan You, Hui-Xiang Chen

In this article, we study Dorroh extensions of algebras and Dorroh extensions of coalgebras. Their structures are described. Some properties of these extensions are presented. We a…

math.RA2019

The structures of Hopf $*$ -algebra on Radford algebras

Hassan Suleman Esmael Mohammed, Hui-Xiang Chen

We investigate the structures of Hopf $*$ -algebra on the Radford algebras over $C$ . All the $*$ -structures on $H$ are explicitly given. Moreover, these Hopf $*$ -algebr…

math.RA2018

Green ring of the category of weight modules over the Hopf-Ore extensions of group algebras

Hua Sun, Hui-Xiang Chen

In this paper, we continue our study of the tensor product structure of category $W$ of weight modules over the Hopf-Ore extensions $k G (χ^{- 1}, a, 0)$ of group algebras $k…

math.RT2018★ 2 cited

Tensor product decomposition rules for weight modules over the Hopf-Ore extensions of group algebras

Hua Sun, Hui-Xiang Chen

In this paper, we investigate the tensor structure of the category of finite dimensional weight modules over the Hopf-Ore extensions $k G (χ^{- 1}, a, 0)$ of group algebras $k G$ . The…

math.CT2018

Reconstruction of tensor categories from their structure invariants

Huixiang Chen, Yinhuo Zhang

In this paper, we study tensor (or monoidal) categories of finite rank over an algebraically closed field $F$ . Given a tensor category $C$ , we have two structure…

math.RT2017★ 1 cited

The Projective Class Rings of a family of pointed Hopf algebras of Rank two

Hui-Xiang Chen, Hassan Suleman Esmael Mohammed, Weijun Lin +1

In this paper, we compute the projective class rings of the tensor product $H_{n} (q) = A_{n} (q) \otimes A_{n} (q^{- 1})$ of Taft algebras $A_{n} (q)$ and $A_{n} (q^{- 1})$ , and its cocycle…

math.RA2017

Green rings of Drinfeld Doubles of Taft algebras

Hua Sun, Hassan Suleman Esmael Mohammed, Weijun Lin +1

In this article, we investigate the representation ring (or Green ring) of the Drinfeld double $D (H_{n} (q))$ of the Taft algebra $H_{n} (q)$ , where $n$ is an integer with $n > 2$ and $q$ …

math.RT2015

Indecomposable decomposition of tensor products of modules over Drinfeld Doubles of Taft algebras

Hui-Xiang Chen, Hassen Suleman Esmael Mohammed, Hua Sun

In this paper, we study the tensor structure of category of finite dimensional representations of Drinfeld quantum doubles $D (H_{n} (q))$ of Taft Hopf algebras $H_{n} (q)$ . Tensor produc…

math.RA2013★ 2 cited

Generalized Hopf-Ore extensions

Lan You, Zhen Wang, Huixiang Chen

We derive necessary and sufficient conditions for an Ore extension of a Hopf algebra to have a Hopf algebra structure of a certain type. This construction generalizes the notion of…

math.RT2013

Representations of Hopf Ore extensions of group algebras and pointed Hopf algebras of rank one

Zhen Wang, Lan You, Hui-Xiang Chen

In this paper, we study the representation theory of Hopf-Ore extensions of group algebras and pointed Hopf algebras of rank one over an arbitrary field $k$ . Let $H=kG(χ, a,\d)$ be…

math.RT2012★ 20 cited

The Green Ring of Drinfeld Double $D (H_{4})$

Hui-Xiang Chen

In this paper, we study the Green ring (or the representation ring) of Drinfeld quantum double $D (H_{4})$ of Sweedler's 4-dimensional Hopf algebra $H_{4}$ . We first give the decomposit…

math.RA2012

Hopf-Ore Extensions and Hopf Algebras of Rank One

Zhen Wang, Lan You, Hui-Xiang Chen

In this paper, we study pointed rank one Hopf algebras and Hopf-Ore extensions of group algebras, over an arbitrary field $k$ . It is proved that the rank of a Hopf-Ore extension of…

math.RT2011★ 2 cited

The Green Rings of Taft algebras

Huixiang Chen, Fred Van Oystaeyen, Yinhuo Zhang

We compute the Green ring of the Taft algebra $H_{n} (q)$ , where $n$ is a positive integer greater than 1, and $q$ is an $n$ -th root of unity. It turns out that the Green ring $r(H_n(…

math.QA2008★ 7 cited

Classification of Quiver Hopf Algebras and Pointed Hopf Algebras of Type One

Shouchuan Zhang, Hui-Xiang Chen, Yao-Zhong Zhang

The quiver Hopf algebras are classified by means of ramification systems with irreducible representations. This leads to the classification of Nichols algebras over group algebras…

math.QA2004

Classification of PM Quiver Hopf Algebras

Shouchuan Zhang, Yao-Zhong Zhang, Hui-Xiang Chen

We describe certain quiver Hopf algebras by parameters. This leads to the classification of multiple Taft algebras as well as pointed Yetter-Drinfeld modules and their correspondin…

The quantum double of the restricted quantum group uq​(sl2​)

The Projective Class Rings of Drinfeld doubles of pointed rank one Hopf algebras

Representations of the Drinfeld doubles of Pointed rank one Hopf algebras

Notes on semisimple tensor categories of rank two

Representations of the small quasi-quantum group

Representations of Drinfeld Doubles of Radford Hopf algebras

Representations of Hopf-Ore extensions of group algebras

Examples of non-semisimple Hopf algebra actions on Artin-Schelter regular algebras

Dorroh extensions of algebras and coalgebras, II

Dorroh extensions of algebras and coalgebras, I

The structures of Hopf ∗-algebra on Radford algebras

Green ring of the category of weight modules over the Hopf-Ore extensions of group algebras

Tensor product decomposition rules for weight modules over the Hopf-Ore extensions of group algebras

Reconstruction of tensor categories from their structure invariants

The Projective Class Rings of a family of pointed Hopf algebras of Rank two

Green rings of Drinfeld Doubles of Taft algebras

Indecomposable decomposition of tensor products of modules over Drinfeld Doubles of Taft algebras

Generalized Hopf-Ore extensions

Representations of Hopf Ore extensions of group algebras and pointed Hopf algebras of rank one

The Green Ring of Drinfeld Double D(H4​)

Hopf-Ore Extensions and Hopf Algebras of Rank One

The Green Rings of Taft algebras

Classification of Quiver Hopf Algebras and Pointed Hopf Algebras of Type One

Classification of PM Quiver Hopf Algebras

The quantum double of the restricted quantum group $u_{q} (s l_{2})$

The structures of Hopf $*$ -algebra on Radford algebras

The Green Ring of Drinfeld Double $D (H_{4})$