Representation Day in USTC (IV)

 

 

2020.10.24 (Saturday), Hefei, China

 

 

The aim of this one-day workshop is to promote academic communication between

algebraists. We are concentrated on the representation theory and related topics in

algebra. Invited speakers are encourage to present their own research or survey recent

progress on a specific topics in algebra

 

 

 

Program:

 

10:00-10:50   Yongjie Wang (Hefei Univ. Tech.)

11:00-11:50   Huanhuan Li (Anhui Univ.)

 

12:00-14:00                Lunch Break

 

14:00-14:50   Lei Du (Anhui Univ.)

15:00-15:50   Zhi Chen (Hefei Univ. Tech.)

 

All lectures will take place at 1318 (Guanli Keyan Building).

 

 

 

Abstracts: available here.

 

 

 

Organizers:  Xiao-Wu Chen, Jue Le, Ren Wang, Yu Ye

 

 

Sponsors:  School of Math. Sci., NNSF, CAS

 

 

 

 

Representation Day in USTC (III)

 

 

2013.7.24 (Wednesday), Hefei, China

 

 

 

Program:

 

 

9:30-10:30    Feng Wei (Beijing Institute of Technology)

11:00-12:00   Shiquan Ruan (Xiamen University) 

 

12:00-14:30                Lunch Break

 

14:30-15:30   Yanhua Wang (Shanghai University of Finance and Ecnomics)

16:00-17:00   Roobeh Hazrat (Univerisy of Western Syndey) 

 

 

 

All lectures will take place at GuanLiKeYan Building, Room 1518.

 

 

 

Abstracts:

 

Feng Wei, Ring-theoretic properties of some noncommutative completed

algebras

 

Abstract: In this talk I will present the structure and ring-theoretic properties

of some non-commuttaive completed algebras. The involved algebras mainly

include Iwasawa algebras, completed Hopf algebras and completed Weyl

algebras. Some known results and open questions will be demonstrated.

 

 

Shiquan Ruan, Tilting bundles and the ``missing part" on the weighted

projective line of type (2, 2, n)

 

Abstract: We classify all the tilting bundles in the category of coherent

sheaves on the weighted projective line of weight type (2, 2, n) , and

investigate the abelianness of the ``missing part" from the category of

coherent sheaves on weighted projective lines to the category of finitely

generated modules on the endomorphism algebra for each tilting bundle.

 

 

Yanhua Wang, Hopf actions on filtered regular algebras

 

Abstract: We study finite dimensional Hopf algebras actions on filtered

Artin-Schelter regular algebras of dimension 2. Results on the Gorenstein

condition and on the global dimension of the corresponding fixed subrings

are provided.

 

 

Roozbeh Hazrat, Graph algebras

 

Abstract: From a graph (e.g., cities and flights between them) one can generate

an algebra which captures the movements along the graph.

 

This talk is about one type of such correspondences, i.e., Leavitt path algebras.

 

Despite being introduced only 8 years ago, Leavitt path algebras have arisen

in a variety of different contexts as diverse as analysis, symbolic dynamics,

noncommutative geometry and representation theory. In fact, Leavitt path

algebras are algebraic counterpart to graph C*-algebras. There are strikingly

 parallel similarities between these two theories. Even more surprisingly,

one cannot (yet) obtain the results in one theory as a consequence of the other;

the statements look the same, however the techniques to prove them are quite

 different (as the names suggest, one uses Algebra and other Analysis).

These all suggest that there might be a bridge between Algebra and Analysis

yet to be uncovered.

 

In this talk, we introduce Leavitt path algebras and then try to understand

the behaviour and to classify them by means of (graded) K-theory.

 

 

Organizers:  Xiao-Wu Chen, Jue Le, Yu Ye

 

Arrival: Take Bus No.10, 129 or 1 from the train station to USTC (中国科学技术大学),

or take a taxi to USTC (east campus, the cross of JinZhai Road and HuangShan Road),

which costs around 20 Yuan.

 

 

Sponsors:  School of Mathematical Sciences, Wu Wen-Tsun Key Lab. of Math., 985 Project,

NNSF, NECT

 

 

Representation Day in USTC (II)

 

 

 

2011.4.2 (Saturday), Hefei, China

 

 

 

Program:

 

 

9:30-10:30    Hualin Huang (Shandong University, Jinan) 

11:00-12:00   Jiafeng Lv (Zhejiang Normal University, Jinhua) 

 

12:00-14:00                Lunch Break

 

14:00-15:00   Can Zhu (Fudan University, Shanghai)

15:20-16:20   Xiaojin Zhang (Nanjing Univeristy of Information Science and Technology, Nanjing) 

16:50-17:50   Zhaoyong Huang (Nanjing University, Nanjing) 

 

 

 

All lectures will take place at GuanLiKeYan Building, Room 1611.

 

 

 

Abstracts:

 

Hualin Huang, Monoidal structures on quiver representations

 

Abstract: We study possible monoidal structures, i.e., natural tensor products, on the category of a

quiver.

 

 

 

Jiafeng Lv, Introduction to piecewise-Koszul algebras

 

Abstract: In this talk, we will talk about piecewise-Koszul algebras, including

nonpure piecewise-Koszul modules/algebras, weakly piecewise-Koszul modules,

quasi-piecewise-Koszul modules/algebras and some applications.

 

 

 

Can Zhu, Hopf actions on Calabi-Yau algebras

 

Abstract:  For a graded automorphism on a graded algebra or a Hopf action

on a graded algebra, homological determinant  is defined, which is a generalization

of the usual determinant of a matrix. By means of homological determinant, we

study the Calabi-Yau property of smash product of a graded Calabi-Yau algebra

with a Hopf algebra. This is joint with Wu Quanshui and Liu Liyu.

 

 

 

Xiaojin Zhang, Cluster tilting for tilted algebras

 

Abstract:  We build a connection between iterated tilted algebras with trivial cluster tilting

and tilted algebras of finite type. As a result, we can classify all tilted algebras with cluster

tilting in terms of quivers, that is, all tilted algebras with cluster tilting are of finite type.

Moreover, we draw the quivers of Auslander's 1-Gorenstein algebras with global dimension

2 admitting trivial cluster tilting subcategories, which implies that such algebras are tilted

of finite type but not Nakayama.

 

 

 

Zhaoyong Huang, Invariant properties of representations under (weak) excellent extensions

 

Abstract:  We introduce the notion of weak excellent extensions of rings as a generalization of 

that of excellent extensions of rings. Let $S$ be a weak excellent extension of an Artinian 

algebra $\Lambda$. We prove that if $\Lambda$ is of finite representation type (resp. 

CM-finite, CM-free), then so is $S$; furthermore, if $S$ is an excellent extension of 

$\Lambda$, then the converse also holds true. We also study when the representation 

dimension of an Artinian algebra is invariant under excellent extensions. It is a joint work

with Juxiang Sun.

 

 

 

 

 

 

 

Organizers:  Xiao-Wu Chen, Jue Le, Yu Ye

 

Arrival: Take Bus No.10, 129 or 1 from the train station to USTC (中国科学技术大学),

or take a taxi to USTC (east campus, the cross of JinZhai Road and HuangShan Road),

which costs around 20 Yuan.

 

Accommodation:  All the invited speakers will stay at the USTC guesthouse (专家楼),

which is near the north door of our east campus. Participants who require accommodation

support should email the organizers.

 

Sponsors:  Math. Department in USTC,Wu Wen-Tsun Key Lab. of Math., 985 Project, NNSF, CAS

 

 

 

 

 

Representation Day in USTC (I)

2010.11.20 (Saturday), Hefei, China

 

 

 

Program:

 

 

9:30-10:30    Jiwei He (Shaoxing University, Shaoxing) 

11:00-12:00   Jiaqun Wei (Nanjing Normal University, Nanjing) 

 

12:00-14:00                Lunch Break

 

14:00-15:00   Yunge Xu (Hubei University, Wuhan)

15:20-16:20   Yanhong Bao (Anhui University, Hefei) 

16:50-17:50   Libin Li (Yangzhou University, Yangzhou) 

 

 

 

All lectures will take place at KeYanGuanLi Building, Room 1611.

 

 

 

Abstracts:

 

Jiwei He, Calabi-Yau property of filtered algebras

 

Abstract: We recall the definitions of Calabi-Yau algebra both in the sense of Kontsevich

and of Ginzburg, and then recall some relations of these two notions. We mainly focus

on the Calabi-Yau property of filtered algebras:  (i) algebras with ascending positive

filtrations; (ii) algebras with descending positive filtrations (the resulting topological

algebra is complete). Among the class (i), we mainly discuss the Calabi-Yau property

of Sridharan algebras; among the class (ii), we mainly discuss the Calabi-Yau property of

noetherian complete algebras by means of coalgebras.

 

 

 

Jiaqun Wei, Semi-tilting complexes

 

Abstract: We introduce the notion of semi-tilting complexes, which is a little generalization

of tilting complexes. Non-trivial semi-tilting complexes exist for any non-semisimple non-local

artin algebras, while tilting complexes may not. We extend interesting results in the tilting theory

to semi-tilting complexes. As corollaries, we also obtain some new characterizations of tilting

complexes.

 

 

Yunge Xu, Hochschild cohomology of truncated quiver algebras

 

Abstract: For a truncated quiver algebra over a field of arbitrary characteristic, we first calculate

its Hochschild cohomology groups, and show that its Hochschild cohomology algebra is

finite- dimensional iff its global dimension is finite iff its quiver has no oriented cycles.

Moreover, based on the minimal projective bimodule resolution, the Gerstenhaber bracket

products on the Hochschild cohomology spaces for truncated quiver algebras are described

explicitly in terms of the combinatorics of the quiver. As a consequence, for truncated basic cycle

algebra A, each element in HH^2(A) defines a noncommutative Poisson structure on A, and

in turn defines the first multiplication of a one-parameter deformation of A.

 

 

 

Yanhong Bao, The cohomology and deformation of Poisson algebras

 

Abstract: For a noncommutative Poisson algebra, we study its quasi-Poisson cohomology,

and introduce its Poisson complex and then its Poisson cohomology. The relation

between the Poisson cohomology and the deformation theory of Poisson algebras

is discussed. This is joint with Yu Ye.

 

 

 

Libin Li, Constructing indecomposable representations over U_q(sl_2) via Ore extension

 

Abstract: In my talk, we shall discuss the infinite dimensional indecomposable representations

over U_q(sl(2)) via Ore extension. We obtain a class of infinite dimensional indecomposable

modules which are not Harish-Chandra modules. This is a joint work with Zhihua Wang.

 

 

 

 

 

Organizers:  Xiao-Wu Chen, Jue Le, Yu Ye

 

Arrival: Take Bus No.10, 129 or 1 from the train station to USTC (中国科学技术大学),

or take a taxi to USTC (east campus, the cross of JinZhai Road and HuangShan Road),

which costs around 20 Yuan.

Accommodation:  All the invited speakers will stay at the USTC guesthouse (专家楼),

which is near the north door of our east campus. Participants who require accommodation

support should email the organizers.

 

Sponsors:  Math. Department in USTC, 985 Project, NNSF