数学科学学院

非交换代数及相关问题研讨会

来源:数学科学学院 发布时间:2021-05-24   758

时间:2021529-530

形式:腾讯会议

5月29日 会议链接:https://meeting.tencent.com/s/zfEVFArkPBje 会议ID:893 331 739

5月30日 会议链接:https://meeting.tencent.com/s/ejviWOvquYrz 会议ID:354 911 987

报告人:丁南庆(南京大学教授)

报告题目:Title: Recent progress on some open problems on envelopes and covers

摘要: The concepts of envelopes and covers of modules have played an important role in the theory of modules and rings and have a great impact on homological algebra, representation theory and commutative algebra. This presentation gives a brief history of the development of envelopes and covers of modules. Some recent progress on this subject will be reviewed and some open problems will be discussed.

 

报告人:李立斌(扬州大学教授)

报告题目:Cell modules of the Green algebras over some Hopf algebras

摘要:Cell modules are very useful to study the representation over the group algebra of Coxeter group and the corresponding Hecke algebra with respect to the Kazhdan-Luszting basis, in general, a positively based algebra. The Green algebra of a Hopf algebra is a positively based algebra with a standard basis of the iso-classes of finite dimensional indecomposable modules over the Hopf algebra. In this talk, we study the structures of the cell modules of the Green algebra R(H) over the Hopf algebra, where H is a pointed rank one Hopf algebra or the Drinfeld quantum double of Sweedler’s 4-dimensional Hopf algebra.  This is joint work with Cao Liufeng and Chen Huixiang.

 

报告人:陈建龙(东南大学教授)

报告题目:Inverses along to an element or two elements

摘要: In 2011, Mary introduced the notion of inverse along to an element, he proved the  Moore-Penrose inverse, Drazin inverse and group inverse are some kind of the inverses along to an element. In 2012, Drazin introduced the notion of (b, c)-inverse, we call it the inverse along to two elements. In particular, the inverse along to an element d is same as (d, d)-inverse. In this talk, we give some progress on the inverses along an element and (b, c)-inverses. Many results unify the results of Moore-Penrose inverses, Drazin inverses, group inverses and inverses along to an element, respectively.

 

报告人:陈惠香(扬州大学教授)

报告题目:Generalized Hopf-Ore extensions

摘要:We investigate some Hopf algebra structures over an Ore extension of a Hopf algebra. The necessary and sufficient conditions for an Ore extension of a Hopf algebra to have a Hopf algebra structure of a certain type is given. This construction generalizes the notion of Hopf-Ore extension, called a generalized Hopf-Ore extension. We describe the generalized Hopf-Ore extensions of the enveloping algebras of Lie algebras. For some Lie algebras $\mathfrak g$, the generalized Hopf-Ore extensions of $U(\mathfrak g)$ are classified.

 

报告人:胡峻(北京理工大学教授)

报告题目:Introduction to Z-graded representation of BGG category O

摘要:In this talk I shall give a brief introduction of Z-graded representation of BGG category O of any semisimple Lie algebras, with a focus on coinvariant algebras, Soergel's V functors and Z-graded lifts of translation functors.

 

报告人:陈良云(东北师范大学教授)

报告题目:Cohomology, extensions, product and complex structures on 3-Bihom-Lie algebras

摘要:In this talk, we mainly introduce cohomology, extensions, product and complex structures on 3-Bihom-Lie algebras.  We introduce representations and cohomologies, construct T*-extensions of quadratic 3-Bihom-Lie algebras and obtain that there is a one-to-one correspondence between equivalent classes of abelian extensions and the second cohomology group.Moreover, we respectively give the necessary and sufficient conditions for the existence of product structures and complex structures of 3-Bihom-Lie algebras.  This talk is a report on joint work with Juan Li.

 

报告人:孙晓松(吉林大学教授)

报告题目: Images of differential operators and derivations

摘要: The study of images of differential operators and derivations of polynomial algebras is closely related to the Jacobian conjecture in affine algebraic geometry. In his talk, we focus on the problem of whether the images of certain differential operators and derivations are the so-called Mathieu subspaces (a generalization of ideals). We will introduce the background, known results, and some of our recent work on this problem.

 

 

联系人:吴志祥(wzx@zju.edu.cn

 

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