2018 Hopf代数研讨会

会议指南

会议日程

报告摘要

通讯录

杭州师范大学理学院

2018.08

会议学术委员会

陈惠香（扬州大学） 胡乃红（华东师范大学）

卢涤明（浙江大学） 李方（浙江大学）

李立斌（扬州大学） 王顶国（曲阜师范大学）

王栓宏（东南大学） 吴泉水 (复旦大学)

吴志祥（浙江大学） 杨士林（北京工业大学）

张良云（南京农业大学） 张印火（Hasselt大学）

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会议指南

一、 会议地点：杭州百瑞国际大酒店（杭州市西湖区教工路 195号）

二、 报到注册：8月 20日在杭州百瑞国际大酒店一楼大厅

三、 报告地点：杭州百瑞国际大酒店三楼百瑞宴会厅

四、 用餐：

早餐：6:30-9:30

中餐：12:00-13:30

晚餐：17:30-19:00

用餐（包括 21日晚宴）均在杭州百瑞国际大酒店三楼百瑞食府

五、 会议联系人： 张印火：yinhuo.zhang@uhasselt.be;

何济位：15067103927，jiweihe@163.com;

俞晓岚：13588809516，xlyu@hznu.edu.cn.

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会议日程

8 月 20 日（周一）

报到注册（地点：杭州百瑞国际大酒店一楼大厅）

8 月 21 日（周二）

时间 报告人 报告题目

08:30-09:00 开幕致辞及合影

09:00-09:40 叶郁 POP and free monoidal categories

09:40-10:10 茶休

10:10-10:50 石聿兴Finite dimensional Hopf algebras over Kac-Paljutkin

algebra H8

11:00-11:40 范中平Some classification results for Hopf algebras of

dimension pqr

12:00-13:30 午餐

14:00-14:40 董井成Slightly-degenerate generalized near-group fusion

categories

14:50-15:30 许勇军Realization of PBW-deformations of type An quantum

groups via multiple Ore extensions

15:30-16:00 茶休

16:00-16:40 张姣 Cyclic homology of strong smash product algebras

16:50-17:30 朱海星 The computation of Brauer group of some Hopf algebra

18:00 晚宴

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8 月 22 日（周三）

时间 报告人 报告题目

08:30-09:10 刘立宇Generalized Weyl algebras arising from Hopf algebra

coactions

09:20-10:00 洪燕勇Uq(sl(m+1))-module algebra structures on the coordinate

algebra of a quantum vector space

10:00-10:30 茶休

10:30-11:10 刘玲

{ , }-Rota-Baxter operators, infinitesimal Hom-

bialgebras and the associative (Bi) Hom-Yang-Baxter

equation

11:20-12:00 方小利Drinfel'd elements and Ribbon elements for quasi-

triangular quasi-Turaev group coalgebras

12:00-13:30 午餐

14:00-14:40 王艳华Zariski cancellation problem for Non-commutative

algebras

14:50-15:30 周贵松Non-commutative Mather-Yau theorem and its

applications to birational geomety

15:30-16:00 茶休

16:00-16:40 陈全国 Hom型 Hopf代数的偏（余）作用

16:50-17:30 王忠伟Separable extensions for crossed products over monoidal

Hom-Hopf algebras

17:30-19:00 晚餐

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8 月 23 日（周四）

时间 报告人 报告题目

08:30-09:10 鲍炎红 Hopf actions and twists of operads

09:20-10:00 陈佳蕾The representations of a class of 2n2 dimensional Hopf

algebras 22nH

10:00-10:30 茶休

10:30-11:10 郑上华The left counital Hopf algebra of free commutative

Nijenhuis algebras

11:20-12:00 高兴 Weighted infinitesimal bialgebras

12:00-13:30 午餐

14:00-14:40 肖占魁 The invariants for quantized symplectic groups

14:50-15:30 杨毓萍 Nichols algebras in twisted Yetter-Drinfeld categories

15:30-16:00 茶休

16:00-16:40 吴金勇Classification of prime regular Hopf algebras of

GK-dimension one

16:50-17:30 刘公祥A classification result on prime Hopf algebras of

GK-dimension one

17:30-19:00 晚餐

8 月 24 日（周五）

离会

ABSTRACT

Hopf actions and twists of operads

Bao, Yanhong

Anhui University

In this talk, we will introduce and study twisting systems and twists of operads.

Based on Hopf actions on operads, we will construct more examples of operads

and extend some classical results in associative algebras to the operadic setting.

This is joint work with Xiao-Wei Xu, Yu Ye, James J. Zhang and Zhi-Bing

Zhao.

The representations of a class of 2n2 dimensional Hopf algebras

H2n2

Chen, Jialei

Beijing University of Technology

In this talk, we present the representations of a class of 2n2 dimensional

semisimple Hopf Algebras H2n2 , which are not pointed, and can be viewed

as a generalization of the 8-dimension Kac-Paljutkin Hopf algebra K8. Al-

l irreducible H2n2-modules are classified and the Grothendieck ring of H2n2

is constructed. Furthermore, we describe the Grothendieck ring r(H2n2) by

generators and relations explicitly.

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Chen, Quanguo

Qufu Normal University

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ÐHom.Hopf�ê� �^Ú {�^nØ.

Slightly-degenerate generalized near-group fusion categories

Dong, Jingcheng

Nanjing University of Information Science and Technology

In this talk, we complete the classification of slightly-degenerate generalized

near-group fusion categories, in terms of Ising categories, Yang-Lee categories,

C(psl2, qt, 8) and braided pointed fusion categories.

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Some classification results for Hopf algebras of dimension pqr

Fan, Zhongping

Ocean University of China

Let p, q, r be distinct prime numbers and k an algebraically closed field of

characteristic zero. We give some new classification results for Hopf algebras

over k of dimension pqr. We prove that Hopf algebras of dimension 42 and 70

are semisimple, which completes the classification for Hopf algebras of these

dimensions.

Drinfel’d elements and Ribbon elements for quasitriangular

quasi-Turaev group coalgebras

Fang, Xiaoli

Shaoxing University

We construct a mirror quasitriangular quasi-Turaev π-coalgebra from a qua-

sitriangular quasi-Turaev π-coalgebra and study the Drinfel’d element from

a new perspective by the gauge transformation of the mirror quasitriangular

quasi-Turaev π-coalgebra. As applications, we use this viewpoint to derive

fundamental properties of the Drinfel’d element and describe some important

properties of a ribbon quasi-Turaev group coalgebra. This is a joint work with

Tae-Hwa Kim and You-Qi Yin.

Weighted infinitesimal bialgebras

Gao, Xing

Lanzhou University

In this talk, we introduce the concept of a weighted infinitesimal bialgebra to

unify the two versions of infinitesimal bialgebras introduced respectively by

Joni-Rota and Loday-Ronco, and then combine it with the concept of an oper-

ated algebra. We also show that some well-known algebras possess a weighted

infinitesimal (unitary) bialgebra, via a construction of the suitable coproducts.

Uq(sl(m+ 1))-module algebra structures on the coordinate

algebra of a quantum vector space

Hong, Yanyong

Zhejiang A&F University

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In this paper, the module-algebra structures of Uq(sl(m+1)) = H(ei, fi, k±1i )1≤i≤m

on the coordinate algebra of quantum vector spaces are studied. We denote

the coordinate algebra of quantum n-dimensional vector space by Aq(n). As

our main result, first, we give a complete classification of module-algebra struc-

tures of Uq(sl(m + 1)) on Aq(3) when ki ∈ Aut L(Aq(3)) as actions on Aq(3)

for i = 1, · · · ,m and m ≥ 2 and with the same method, on Aq(2), all module-

algebra structures of Uq(sl(m + 1)) are characterized. Lastly, the module-

algebra structures of Uq(sl(m+ 1)) on Aq(n) are obtained for any n ≥ 4. This

work is done with S. Duplij and F. Li.

A classification result on prime Hopf algebras of

GK-dimension one

Liu, Gongxiang

Nanjing University

Based on our previous work, we want to give a try to classify prime Hopf

algebras of GK-dimension one without requirement on regularity. Some appli-

cations will be given too.

Generalized Weyl algebras arising from Hopf algebra coactions

Liu, Liyu

Yangzhou University

There are many examples of generalized Weyl algebra (originally defined by

Vladimir Bavula) in the field of Hopf algebra, especially some coinvariants

of Hopf algebra coactions. In this talk, I will give a necessary and sufficient

condition that a generalized Weyl algebra over a polynomial algebra in one or

two variables is twisted Calabi-Yau.

{σ, τ}-Rota-Baxter operators, infinitesimal Hom-bialgebras and

the associative (Bi)Hom-Yang-Baxter equation

Liu, Ling

Zhejiang Normal University

A {σ, τ}-Rota-Baxter operator is a sort of twisted version of a Rota-Baxter

operator of weight zero. We show how to obtain a certain particular case

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of {σ, τ}-Rota-Baxter operator from a solution of the associative (Bi)Hom-

Yang-Baxter equation and a Hom-pre-Lie algebra from an infinitesimal Hom-

bialgebra.

Finite dimensional Hopf algebras over Kac-Paljutkin algebra

H8

Shi, Yuxing

Jiangxi Normal University

By the Lifting method introduced by Andruskiewitsch and Schneider in 1998,

we obtained five families of new finite dimensional Hopf algebras over H8.

Their corresponding Nichols algebras are of Cartan types A1, A2, and some

products of them.

Zariski cancellation problem for non-commutative algebras

Wang, Yanhua

Shanghai University of Finance and Economics

I will give some recent developments on the Zariski cancellation problem of

noncommutative algebras.

Separable extensions for crossed products over monoidal

Hom-Hopf algebras

Wang, Zhongwei

Jinling Institute of Technology

Let (H,α) be a Frobenius monoidal Hom-Hopf algebra, and (A, β) an (H∗, α∗−1)-

Hom-Hopf Galois extension of (AH , β|AH ). We prove that the separability of

the Hom-algebra extension A/AH is equivalent to the existence of a trace one

element ω ∈ CA#H(A) that centralizes A. As applications, we obtain the dif-

ferentiated conditions for the extension A#σH/A to be separable, and deduce

a Doi’s result of Hom-type.

Classification of prime regular Hopf algebras of GK-dimension

one

Wu, Jinyong

Weizhou University

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The classification of affine prime regular Hopf algebras of GK-dimension one

is completed. As consequences, we show that there do exist prime regular

Hopf algebras of GK-dimension one which are not pointed and without the

Chevalley property.

The invariants for quantized symplectic groups

Xiao, Zhankui

Huaqiao University

In this talk we present a categorical version of the first and second fundamental

theorems of the invariant theory for the quantized symplectic groups. Our

methods depend on the theory of braided strict monoidal categories which are

pivotal, more explicitly the diagram category of framed tangles. This is joint

work with Yuping Yang and Yinhuo Zhang.

Realization of PBW-deformations of type An quantum groups

via multiple Ore extensions

Xu, Yongjun

Qufu Normal University

The notion of multiple Ore extension is introduced as a natural generaliza-

tion of Ore extensions and double Ore extensions. For a PBW-deformation

Bq(sl(n + 1, C)) of type An quantum group, we explicitly obtain the com-

mutation relations of its root vectors, then show that it can be realized via

a series of multiple Ore extensions, which we call a ladder Ore extension of

type (1, 2, · · · , n). Moreover, we analyze the quantum algebras Bq(g) with g of

type D4, B2 and G2 and give some examples and counterexamples that can be

realized by a ladder Ore extension. This is a joint work with Hua-Lin Huang

and Dingguo Wang.

Nichols algebras in twisted Yetter-Drinfeld categories

Yang, Yuping

Southwest University

Nichols algebras are basic objects in the study of pointed Hopf algebras and

pointed tensor categories. In this talk, I will introduce some basic notions,

examples and research problems on Nichols algebras. Some recent works on the

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classification of finite-dimensional Nichols algebras in twisted Yetter-Drinfeld

categories associated to abelian groups will also be introduced.

POP and free monoidal categories

Ye, Yu

University of Science and Technology of China

Joyal and Street provided a mathematical framework for the tensor calculus

in monoidal categories by using progressive plane graphs. In this talk, we will

reformulate their work in a purely combinatoric framework. We introduce the

notion of POP (planarly ordered progressive graph), and apply to construct

free strict monoidal categories on tensor schemes.

Cyclic homology of strong smash product algebras

Zhang, Jiao

Shanhai University

For any strong smash product algebra of two algebras A and B with a bijective

morphism R, we construct a cylidrica module whose diagonal cyclic module is

graphically proven to be isomorphic to the cyclic module of the strong smash

product algebra. A spectral sequence is established to converge to the cyclic

homology of the strong smash product algebra. Exampls are provided to show

how our results work. Particularly, the cyclic homology of the Pareigis’ Hopf

algebra is obtained in the way.

The left counital Hopf algebra of free commutative Nijenhuis

algebras

Zheng, Shanghua

Jiangxi Normal University

Motivated by the Hopf algebra structures established on free commutative

Rota-Baxter algebras, we explore Hopf algebra related structures on free com-

mutative Nijenhuis algebras. Applying a cocycle condition, we first prove that

a free commutative Nijenhuis algebra on a left counital bialgebra (in the sense

that the right-sided counicity needs not hold) can be enriched to a left couni-

tal bialgebra. We then establish a general result that a connected graded left

counital bialgebra is a left counital right antipode Hopf algebra in the sense

that the antipode is also only right-sided. We finally apply this result to show

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that the left counital bialgebra on a free commutative Nijenhuis algebra on

a connected left counital bialgebra is connected and graded, hence is a left

counital right antipode Hopf algebra.

Noncommutative Mather-Yau theorem and its applications to

birational geomety

Zhou, Guisong

Ningbo Institute of Technology, Zhejiang University

In this talk, we will show that the equivalence class of a superpotential up to

formal change of variables, is determined by its polarized Jacobi algebra as-

suming it is finite dimensional. This result can be viewed as a noncommutative

analogue of the famous theorem of Mather and Yau on isolated hypersurface

singularities. As one of its applications, we will present a rigidity theorem

on the relative singularity categories and the classical singularity categories of

3-dimensional flopping contractions. It provides an evidence for the Donovan-

Wemyss conjecture, which asserts that the contraction algebra is a complete

invariant for the underlying singularities of 3-dimensional flopping contraction-

s. This is a joint work with Zheng Hua of HongKong University.

The computation of Brauer group of some Hopf algebra

Zhu, Haixing

Nanjing Forestry University

In this talk, we will foucs on the computation of Brauer group of some Hopf al-

gebra. We will show that the group of braided autoequivalences of the category

of H-comodules is isomorphic to the group of braidedcommutative bi-Galois

objects. As an application, we obtain the group of braided autoequivalences

of the representation category of Lusztig’s quantum group uq(sl(2))′, where q

is a root of unity of odd order, and thus the corresponding Brauer group.

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