Yinhuo Zhang

activity

20052026

most citedDeformations of Koszul Artin-Schelter Gorenstein algebras

11 citations · 60 across the 46 of their papers we have counts for

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Showing math.QAShow all

22 papers · 1 filter

math.QA2026

Notes on gamma invariants of finite dimensional Hopf algebras

Xinru Zhang, Libin Li, Yinhuo Zhang

Let $H$ be a finite-dimensional, non-semisimple Hopf algebra over an algebraically closed field $k$ . This paper investigates the asymptotic behavior of the core of left $H…

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

Noetherian pointed Hopf algebras are affine

Huan Jia, Yinhuo Zhang

Let $k$ be a field. In this paper, we introduce the notions of $reduction order$ and $reduction-factorization$ on words, and use them to show that any right or le…

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.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

Quotient Hopf algebras of the free bialgebra with PBW bases and GK-dimensions

Huan Jia, Naihong Hu, Rongchuan Xiong +1

Let $K$ be a field. We study the free bialgebra $T$ generated by the coalgebra $C = K g \oplus K h$ and its quotient bialgebras (or Hopf algebras…

math.QA2017

On nondiagonal finite quasi-qantum groups over finite abelian groups

Hua-Lin Huang, Yuping Yang, Yinhuo Zhang

In this paper, we initiate the study of nondiagonal finite quasi-quantum groups over finite abelian groups. We mainly study the Nichols algebras in the twisted Yetter-Drinfeld modu…

math.QA2017

Finite-dimensional quasi-Hopf algebras of Cartan type

Yuping Yang, Yinhuo Zhang

In this paper, we present a general method for constructing finite-dimensional quasi-Hopf algebras from finite abelian groups and braided vector spaces of Cartan type. The study of…

math.QA2016★ 5 cited

On the center of the quantized enveloping algebra of a simple Lie algebra

Libin Li, Limeng Xia, Yinhuo Zhang

Let $g$ be a finite dimensional simple complex Lie algebra and $U = U_{q} (g)$ the quantized enveloping algebra (in the sense of Jantzen) with $q$ being generic. In this p…

math.QA2015

The octonions form an Azumaya algebra in certain braided linear Gr-categories

T. Cheng, H. Huang, Y. Yang +1

By applying the idea of viewing the octonions as an associative algebra in certain tensor categories, or more precisely as a twisted group algebra by a 2-cochain, we show that the…

math.QA2014★ 3 cited

Braided autoequivalences and the equivariant Brauer group of a quasitriangular Hopf algebra

Jeroen Dello, Yinhuo Zhang

Let $(H, R)$ be a finite dimensional quasitriangular Hopf algebra over a field $k$ , and $_{H} M$ the representation category of $H$ . In this paper, we study the braided auto…

math.QA2014

Representations of the small quasi-quantum group $Q u_{q} (sl_{2})$

Gongxiang Liu, Fred Van Oystaeyen, Yinhuo Zhang

The quasi-Frobenius-Lusztig kernel $Q u_{q} (sl_{2})$ associated with $sl_{2}$ has been constructed in \cite{Liu}. In this paper we study the represe…

math.QA2013★ 1 cited

Braided autoequivalences and quantum commutative bi-Galois objects

Yinhuo Zhang, Haixing Zhu

Let $(H, R)$ be a quasitriangular weak Hopf algebra over a field $k$ . We show that there is a braided monoidal equivalence between the Yetter-Drinfeld module category $^H_H\mathscr{…

math.QA2013

Structure theorems for bicomodule algebras over quasi-Hopf algebras, weak Hopf algebras and braided Hopf algebras

Jeroen Dello, Florin Panaite, Freddy Van Oystaeyen +1

Let H be a quasi-Hopf algebra, a weak Hopf algebra or a braided Hopf algebra. Let B be an H-bicomodule algebra such that there exists a morphism of H-bicomodule algebras v:H\righta…

math.QA2013★ 2 cited

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 $g$ .

math.QA2013★ 2 cited

The Green rings of pointed tensor categories of finite type

Hua-Lin Huang, Fred Van Oystaeyen, Yuping Yang +1

In this paper, we compute the Clebsch-Gordan formulae and the Green rings of connected pointed tensor categories of finite type.

math.QA2012

Calabi-Yau Nichols algebras of Hecke type

Xiaolan Yu, Yinhuo Zhang

Let $R$ be a Nichols algebra of Hecke type. In this paper, we show that if $R$ is Noetherian and of finite global dimension, then $R$ has a rigid dualizing complex. We then give a…

math.QA2011★ 1 cited

The Calabi-Yau property of Hopf algebras and braided Hopf algebras

Xiaolan Yu, Yinhuo Zhang

Let $H$ be a finite dimensional semisimple Hopf algebra and $R$ a braided Hopf algebra in the category of Yetter-Drinfeld modules over $H$ . When $R$ is a Calabi-Yau algebra, a nece…

math.QA2011★ 3 cited

Calabi-Yau pointed Hopf algebras of finite Cartan type

Xiaolan Yu, Yinhuo Zhang

We study the Calabi-Yau property of pointed Hopf algebra $U(\mc{D},\lmd)$ of finite Cartan type. It turns out that this class of pointed Hopf algebras constructed by N. Andruskiewi…

math.QA2011

Ext algebra of Nichols algebras of type $A_{2}$

Xiaolan Yu, Yinhuo Zhang

We give the full structure of the Ext algebra of a Nichols algebra of type $A_{2}$ by using the Hochschild-Serre spectral sequence. As an application, we show that the pointed Hopf a…

math.QA2005

Quantum double of ${\rm U}_q((\ksl_2)^{\leq 0})$

Jun Hu, Yinhuo Zhang

Let $U_{q} (s l_{2})$ be the quantized enveloping algebra associated to the simple Lie algebra $s l_{2}$ . In this paper, we study the quantum double $D_{q}$ of the Borel subalgebra ${U}_q((…

math.QA2005★ 1 cited

Cocycle Deformations and Brauer Group Isomorphisms

Huixiang Chen, Yinhuo Zhang

Let $H$ be a Hopf algebra over a commutative ring $k$ with unity and $σ : H \otimes H ⟶ k$ be a cocycle on $H$ . In this paper, we show that the Yetter-Drinfeld module cat…

Notes on gamma invariants of finite dimensional Hopf algebras

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

Noetherian pointed Hopf algebras are affine

Representations of the Drinfeld doubles of Pointed rank one Hopf algebras

Representations of the small quasi-quantum group

Quotient Hopf algebras of the free bialgebra with PBW bases and GK-dimensions

On nondiagonal finite quasi-qantum groups over finite abelian groups

Finite-dimensional quasi-Hopf algebras of Cartan type

On the center of the quantized enveloping algebra of a simple Lie algebra

The octonions form an Azumaya algebra in certain braided linear Gr-categories

Braided autoequivalences and the equivariant Brauer group of a quasitriangular Hopf algebra

Representations of the small quasi-quantum group Quq​(sl2​)

Braided autoequivalences and quantum commutative bi-Galois objects

Structure theorems for bicomodule algebras over quasi-Hopf algebras, weak Hopf algebras and braided Hopf algebras

Quasi-Frobenius-Lusztig kernels for simple Lie algebras

The Green rings of pointed tensor categories of finite type

Calabi-Yau Nichols algebras of Hecke type

The Calabi-Yau property of Hopf algebras and braided Hopf algebras

Calabi-Yau pointed Hopf algebras of finite Cartan type

Ext algebra of Nichols algebras of type A2​

Quantum double of ${\rm U}_q((\ksl_2)^{\leq 0})$

Cocycle Deformations and Brauer Group Isomorphisms

Representations of the small quasi-quantum group $Q u_{q} (sl_{2})$

Ext algebra of Nichols algebras of type $A_{2}$