李理论迷你论坛（苏州◎在线）

1.     报告题目: Super Knizhnik-Zamolodchikov Equations and the Representations of Lie Superalgebras

报告人: 曹彬涛教授（云南大学）

报告时间: 2021年6月26日, 8: 00--8: 50

报告地点：腾讯会议ID:378 1657 2409 会议密码: 202106

报告摘要: We establish an explicit bijection between the sets of singular solutions of the (super) KZ equations associated to the Lie superalgebra, of infinite rank, of type $\mf{a, b,c,d}$ and to the corresponding Lie algebra. As a consequence, the singular solutions of the super KZ equations associated to the classical Lie superalgebra, of finite rank, of type $\mf{a, b,c,d}$ for the tensor product of certain parabolic Verma modules (resp., irreducible modules) are obtained from the singular solutions of the KZ equations for the tensor product of the corresponding parabolic Verma modules (resp., irreducible modules) over the corresponding Lie algebra of sufficiently large rank, and vice versa. This is a joint work with Prof. Ngau Lam.

2.     报告题目: Realization of irreducible A_1^{(1)}-modules in Chari’s category \tilde{O}

报告人: 陈福林教授（厦门大学）

报告时间: 2021年6月26日, 9: 00--9: 50

报告地点：腾讯会议ID:378 1657 2409 会议密码: 202106

报告摘要:. In this talk, we will report a recent work joint with Yun Gao and Shaobin Tan on the free field realization of irreducible A_1^{(1)}-modules in Chari’s category \tilde{O}.  We will also mention a free field realization of Harish-Chandra modules for certain current algebras of sl_2.

3.     报告题目: A family of modules over the Rueda's algebras

报告人: 陈洪佳教授（中国科学技术大学）

报告时间: 2021年6月26日, 10: 00--10: 50

报告地点：腾讯会议ID:378 1657 2409 会议密码: 202106

报告摘要: In this talk, I will first give a brief introduction of the U(h)-free module theory over Lie and associative algebras with triangular decompositions. Some recent results on this topic will be presented. In the second part of the talk, I will introduce the joint work with L. Wang about the R_0-free modules for the Rueda's algebra R where R_0 is the “Cartan part” of the associative algebra R. The review part is mostly based on works by Y. Cai, X. Guo, G. Liu, R. Lv, J. Nilsson, H. Tan, K. Zhao, etc.

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

报告人: 陈良云教授（东北师范大学）

报告时间: 2021年6月26日, 11: 00--11: 50

报告地点：腾讯会议ID:378 1657 2409 会议密码: 202106

报告摘要:. 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.

5.     报告题目: The McKay-Slodowy correspondence and Poincar\'{e} series of the relative groups

报告人:  王丹霞博士（湖州师范学院）

报告时间: 2021年6月26日,14: 00--14: 50

报告地点：腾讯会议ID: 892 6594 0009 会议密码：202106

报告摘要: Let $N$ be a normal subgroup of a finite group $G$ and $V$ be a fixed finite-dimensional $G$-module. The Poincar\'{e} series for the multiplicities of induced modules and restriction modules in the tensor algebra and symmetric algebra are studied in connection with the McKay-Slodowy correspondence. Moreover, we obtain some results of the affine Lie algebras associated with the distinguished pairs of subgroups of $\mathrm{SU}_2$. This talk is based on the joint work with Professors N. Jing and H. Zhang.

6.     报告题目: Diagonal coset of affine vertex operator algebras

报告人: 林兴君教授（武汉大学）

报告时间: 2021年6月26日, 15: 00--15: 50

报告地点：腾讯会议ID: 892 6594 0009 会议密码：202106

报告摘要: Coset construction is one of important ways to construct new vertex operator algebras. In this talk, we will talk about the classification of irreducible modules of diagonal coset of affine vertex operator algebras. We will also talk about some results about fusion rules of diagonal coset of affine vertex operator algebras.

7.     报告题目: Representations  for the N=1 super-BMS$_3$ algebra

报告人: 刘东教授（湖州师范学院）

报告时间: 2021年6月26日, 16: 00--16: 50

报告地点：腾讯会议ID: 892 6594 0009 会议密码：202106

报告摘要: In this talk, we give a construction of simple modules generalizing both highest weight and Whittaker modules for the super-BMS algebra, in the spirit of the work of Mazorchuk and Zhao on simple Virasoro modules.   We establish a 1-1 correspondence

between simple restricted modules  and simple modules of a family of finite dimensional

solvable Lie superalgebras associated to the super-BMS algebra.

8.     报告题目: Quantum i-Schur superalgebras and their semisimplicity criteria

报告人: 罗栗教授（华东师范大学）

报告时间: 2021年6月26日, 17: 00--17: 50

报告地点：腾讯会议ID: 892 6594 0009 会议密码：202106

报告摘要:. We introduce the notion of quantum i-Schur superalgebra , which is a type B/C counterpart of the quantum Schur superalgebra. Imitating the geometric realization of quantum Schur algebras  due to Beilinson-Lusztig-MacPherson, we obtain multiplication formulas for these superalgebras. As an application, these formulas are used to derive a semisimplicity criteria of quantum i-Schur superalgebras. This is joint work with my student Jian Chen.

9.     报告题目:  Represenations of truncated  polynomial Virasoro  algebras

报告人: 裴玉峰教授（上海师范大学）

报告时间: 2021年6月27日, 8: 00--8: 50

报告地点：腾讯会议ID:378 1657 2409 会议密码: 202106

报告摘要: In this talk, we study a category of restricted modules for truncated polynomial Virasoro algebras. We  characterize simple modules in this category.  Free field realizations of certain restricted modules are constructed using Heisenberg vertex algebras.

10.  报告题目: Twisted tensor products of $\phi$-coordinated modules for nonlocal vertex algebras

报告人: 孙建才教授（上海大学）

报告时间: 2021年6月27日, 9: 00--9: 50

报告地点：腾讯会议ID:378 1657 2409 会议密码: 202106

报告摘要: We study twisted tensor products of $\phi$-coordinated modules of nonlocal vertex algebras. Furthermore, we introduce the notion of $\phi$-coordinated module twistor for a $\phi$-coordinated module of a nonlocal vertex algebra.

11.  报告题目: Graded cluster algebras arising from marked surfaces with puncture

报告人: 唐孝敏教授（黑龙江大学）

报告时间: 2021年6月27日, 10: 00--10: 50

报告地点：腾讯会议ID:378 1657 2409 会议密码: 202106

报告摘要: Cluster algebras were conceived by Fomin and Zelevinsky  in 2000 as a tool for studying dual canonical bases and total positivity in semisimple Lie groups and their quantum analogs. However, the theory of cluster algebras has since taken on a life of its own, as connections and applications have been discovered in diverse areas of mathematics, including representation theory of quivers and finite dimensional algebras,  Poisson geometry , string theory, discrete dynamical systems and integrability, and combinatorics. Gradings for cluster algebras have been introduced in various ways by a number of authors and for a number of purposes.  Recently,  Booker-Price T in [J. Algebra, 2020, 560: 89-113]  study the gradings arising from triangulations of marked bordered 2-dimensional surfaces without puncture.  In this paper, we mainly study the degree of triangulation of marked bordered 2-dimensional surfaces with puncture.  We  give a valuation functions on such a surface by using the methods of [Acta Math., 2008, 21:83-146] and [J. Algebr. Comb., 2015, 42: 1111-1134]. We give two examples to illustrate the theory and show that each homogeneous space has finitely many variables.  This work is jont with Dr. Yongyue Zhong.

12.  报告题目:Double-bosonization construction theorem for irregular R-matrices

报告人: 胡红梅博士（苏州科技大学）

报告时间: 2021年6月27日, 11: 00--11: 50

报告地点：腾讯会议ID:378 1657 2409 会议密码: 202106

报告摘要: This is a joint work with Prof. Naihong Hu. We will build up the related theory of weakly quasitriangular dual pairs suitably for non-standard R-matrices (irregular), and establish the generalized double-bosonization construction for irregular R-matrices, which generalizes Majid's results for regular R-matrices. As an application, we will take about the type-crossing construction for the exceptional quantum group of type G₂. This affirms Majid's expectation that the tree structure of nodes diagram associated with quantum groups can be grown out of the node corresponding to  Uq(sl2) by the (generalized) double-bosonization procedures.

13.  报告题目: Vertex algebras and extended affine Lie algebras coordinated by rational quantum tori

报告人: 王清教授（厦门大学）

报告时间: 2021年6月27日,14: 00--14: 50

报告地点：腾讯会议ID: 892 6594 0009 会议密码：202106

报告摘要: In this talk, we establish a natural connection between the EALA $\widehat{sl_N}(C_q)$ coordinated by the rational quantum 2-tori $C_q$ with vertex algebra through twisted modules. This is a joint work with Fulin Chen, Xiaoling Liao and Shaobin Tan.

14.  报告题目: Some results on Lie conformal algebras of Block type

报告人: 夏春光教授（中国矿业大学）

报告时间: 2021年6月27日, 15: 00--15: 50

报告地点：腾讯会议ID: 892 6594 0009 会议密码：202106

报告摘要: In this talk, we will give some results on Lie conformal algebras of Block type. We classify finite irreducible conformal modules over a class of infinite Lie conformal algebras of Block type and their N=1,2 super generalizations. The extension problem for conformal modules is also completely solved. This talk is mainly based on the joint work with Y. Su and L. Yuan.

15.  报告题目: 李(超)代数的多项式模

报告人: 夏利猛教授（江苏大学）

报告时间: 2021年6月27日, 16: 00--16: 50

报告地点：腾讯会议ID: 892 6594 0009 会议密码：202106

报告摘要: 介绍李代数李超代数的多项式模的一些基础知识。介绍一个GIM李代数的秩1的多项式模的分类及其单性条件.

16. 报告题目: 6A-algbera and its representations

报告人: 余铌娜教授（厦门大学）

报告时间: 2021年6月27日, 17: 00--17: 50

报告地点：腾讯会议ID: 892 6594 0009 会议密码：202106

报告摘要: An Ising vector in a vertex operator algebra is a Virasoro vector which generates a subalgebra isomorphic to the Virasoro vertex operator algebra L(\frac{1}{2},0). It is believed that any subVOA generated by two Ising vectors is uniquely determined by their inner products. In this talk, I will talk about the structure and representation of a 6A-algebra which is a vertex operator algebra generated by two Ising vectors e,f with inner product \left\langle e,f\right\rangle =\frac{5}{2^{10}}. In particular, I will talk about the uniqueness of the vertex operator algebra structure of this 6A-algebra, classification of the irreducible modules, and the fusion rules. This is a joint work with C. Dong and X. Jiao.

邀请人：吕仁才