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  • 天元讲堂(8.6)代数系列学术报告
  • 浏览量:276 发布人:佚名 发布时间:2017-08-03 13:52:05
  • 题目:An Introduction to pre-Lie algebras

    报告人:白承铭教授(南开大学)

    时间:2017868:30-9:20

    地点:本部览秀楼105

    摘要:We give a brief introduction to the study of pre-Lie algebras, emphasizing the relationships with other topics in mathematics and mathematical physics

     

    题目Universal central extensions of $\mathfrak{sl}_{m|n}$ over $\mathbb{Z}/2\mathbb{Z}$-graded algebras

    报告人:陈洪佳教授(中国科技大学)

    时间:201786 9:30-10:20

    地点:本部览秀楼105

    摘要::In this talk central extensions of the Lie superalgebra $\mathfrak{sl}_{m|n}(A)$ are constructed, where $A$ is a $\mathbb{Z}/2\mathbb{Z}$-graded superalgebra over a commutative ring $K$. The Steinberg Lie superalgebra $\mathfrak{st}_{m|n}(A)$ plays a crucial role. We show that $\mathfrak{st}_{m|n}(A)$ is a central extension of $\mathfrak{sl}_{m|n}(A)$ for $m+n\geq 3$. We use a $\mathbb{Z}/2\mathbb{Z}$-graded version of cyclic homology to show that the center of the extension is isomorphic to $\mathrm{HC}_1(A)$ as $K$-modules. For $m+n\geq 5$, we prove that $\mathfrak{st}_{m|n}(A)$ is the universal central extension of $\mathfrak{sl}_{m|n}(A)$. For $m+n=3,4$, we prove that $\mathfrak{st}_{2|1}(A)$ and $\mathfrak{st}_{3|1}(A)$ are both centrally closed. The universal central extension of $\mathfrak{st}_{2|2}(A)$ is constructed explicitly. This is a joint work with Jie Sun.

     

    题目:16-fold way conjecture and vertex operator superalgebras

    报告人:董崇英教授(University of California, Santa Cruz

    时间: 201786 10:30-11:20

    地点:本部览秀楼105

    摘要:This talk will discuss the modular category for a vertex operator subperalgebras and its connection with the 16-fold way conjecture in category theory. The is a joint work with Richard Ng and Li Ren.

     

     

    题目:Matsuo algebras and vertex operator algebras(I)

    报告人:姜翠波教授(上海交通大学)

    时间:20178611:30-12:20

    地点:本部览秀楼105

    摘要: We will talk about Matsuo algebras and related vertex operator algebras. We also give classification of simple vertex operator algebras generated by Ising vectors of sigma-type. This is a joint work with Ching Hung Lam and Hiroshi Yamauchi.

     

    题目:Hopf algebra structure for quantum toroidal algebras

    报告人:景乃桓教授(上海大学&North Carolina State University)

    时间: 20178613:20-14:10

    地点:本部览秀楼105

    摘要:Quantum toroidal algebras are generalization of quantum affine algebras, ie, certain deformation of the central extension of the toroidal algebra of maps from $C[s, t, s^{-1}, t^{-1}]$ to a simple Lie algebra. Drinfeld has defined a second Hopf algebra structure for the completion of the quantum affine algebra, which can be generalized to the completion of the quantum toroidal algebra. I will  discuss the recent development to show that the quantum toroidal algebra has a finite Hopf algebra structure. We also derived the comultiplication formula for the Drinfeld generators of the quantum toroidal algebra in the type A (joint work with Honglian Zhang).

     

    题目:Quantum vertex algebras and their representations of different types

    报告人:李海生教授( Rutgers University )

    时间: 20178614:20-15:10

    地点:本部览秀楼105

    摘要:This talk is about quantum vertex algebras and their representations. First, we shall briefly discuss Frenkel-Reshetikhin's notion of deformed chiral algebra, Etingof and Kazhdan's notion of quantum vertex operator algebra, and then we discuss in detail the notion of quantum vertex algebra we have introduced and studied for a few years.  Second, we present the basic results in this theory, including the conceptual construction of weak quantum vertex algebras and their modules. Third, we discuss the theories of quasi modules and $\phi$-coordinated modules, and we explain how to use these theories to associate quantum vertex algebras to various (quantum) algebras.

     

    题目:Pseudo-tensor categories and vertex operator representations

    报告人:林宗柱教授(Kansas State University)

    时间: 20178615:20-16:10

    地点:本部览秀楼105

    摘要:Beilinson and Drinfeld defined Pseudo-tensor categories to be be a category which has a features of a tensor category but not necessarily have the actual tensor products. In the talk we discuss the category of or representations of a vertex operator algebrasand discuss the pseudo-tensor category structure.

     

    题目:Highest Weight Vectors of Mixed Tensor Products of General Linear Lie Superalgebras

    报告人:苏育才教授(同济大学)

    时间: 20178616:20-17:10

    地点:本部览秀楼105

    摘要:A notion of cyclotomic (or level $k$) walled Brauer algebras ${\mathcal B}_{k,r,t}$ is present for arbitrary positive integer $k$. It is proven that ${\mathcal B}_{k,r,t}$ is free over a commutative ring with rank $k^{r+t}(r+t)!$ if and only if it is admissible in some sense. Using super Schur-Weyl duality between general linear Lie superalgebras ${\frak{gl}}_{m|n}$ and ${\mathcal B}_{2,r,t}$, we give a classification of highest weight vectors of ${\frak{gl}}_{m|n}$-modules $M^{rt}_{pq}$, the tensor products of Kac-modules with mixed tensor products of the natural module and its dual. This enables us to establish an explicit relationship between ${\frak{gl}}_{m|n}$-Kac-modules and right cell (or standard) ${\mathcal B}_{2,r,t}$-modules over $\mathbb C$. Further, we find an explicit relationship between indecomposable tilting ${\frak{gl}}_{m|n}$-modules appearing in $M^{rt}_{pq}$, and principal indecomposable right ${\mathcal B}_{2,r,t}$-modules via the notion of Kleshchev bipartitions. As an application, decomposition numbers of ${\mathcal B}_{2,r,t}$ arising from super Schur-Weyl duality are determined. This is a joint work with Hebing Rui.

     

    题目:The Automorphism Group of Parafermion Vertex Operator Algebras

    报告人:王清教授(厦门大学)

    报告时间: 20178617:20-18:10

    地点:本部览秀楼105

    摘要:The full automorphism group of parafermion VOA associated to an integrable highest weight module for any affine Kac-Moody algebras is determined. This is a joint work with Andrew R. Linshaw.

     
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