Xiamen Workshop on Lie Algebras

Schedule

June 8，Room 661, Building of Mathematics Physics, Haiyun Campus

Abstracts

June 8，Saturday

苏育才: Mixed Cohomology of Lie Superalgebras

Abstract: Supermanifolds are known to admit both differential forms and integral formsthus any appropriate super analogue of the de Rham theory should take bothtypes of forms into account. However, the cohomology of Lie superalgebras studied so far in the literature involves only differential forms when interpreted as a de Rham theory for Lie supergroups. Thus a new cohomologytheory of Lie superalgebras is needed to fully incorporate differential integral forms, and we investigate such a theory here. This new cohomology is defined by a BRST complex of Lie superalgebra modules, and includes thestandard Lie superalgebra cohomology as a special case. General properties expected of a cohomology theory are established for the new cohomology, andexamples of the new cohomology groups are computed. This is a joint work with R.B. Zhang.

陈良云：On derivations,  biderivations  and  triple homomorphisms for certain Jordan algebras

Abstract: In this talk, I will introduce several results on derivations, biderivations  and  triple homomorphisms for certain Jordan algebras.  For the semi-simple Jordan algebras over a field of characteristic 0, we give the sufficient necessary conditions that their derivation algebras are simple. For more general ones, perfect Jordan algebras, we focus on their biderivations triple homomorphisms. We describe biderivations by the centroid on a perfect centerless Jordan algebra. We also study the relation between homomorphisms triple homomorphisms on perfect Jordan algebras, give a sufficient necessary condition for a  triple homomorphism to be a homomorphism.  This is a joint work with Chenrui Yao Yao Ma.   

陈福林: Realizations of $A_1^{(1)}$-modules in category $\wt{\mathcal O}$ Harish-Chandra modules of current algebras

Abstract: Associated to any $\C$-valued linear function on $\C[t]_S$ (localization of $\C[t]$ at $S$), one may define a notion of highest weight module for the current algebra $\mathfrak{sl}_2(\C)\ot \C[t]_S$ with the values of the function as structure constants. In this paper,  we give a  free field construction of highest weight $\mathfrak{sl}_2(\C)\ot \C[t]_S$-modules with finite weight multiplicities.

Using this a result of Jakobsen-Kac, we obtain an explicit realization of all irreducible highest weight$\mathfrak{sl}_2(\C)\ot \C[t]_S$-modules.Consequently,  we  obtain:

(i) an explicit realization of all irreducible modules in Chari's category $\wt{\mathcal O}$ for the affine Kac-Moody Lie algebra $A_{1}^{(1)}$;

 (ii) an explicit realization of allsimple weight modules for $\mathfrak{sl}_2(\C)\ot \C[t]_S$ with finite weight multiplicities.

陈志玮: Simple supermodules for Lie superalgebras

Abstract: A Lie superalgebra is a generalization of a Lie algebra to include a Z/2-grading. In this talk, we will  explain the connection between simple supermodules over Lie superalgebras simple modules over their   underlying Lie algebras. In particular, the classification of simple supermodules can be reduced to the classification of simple modules over the underlying Lie algebra of type A.

张贺春:  Tensor product of $\mathcal C_q [SL_2]$-modules

Abstract: There are four types of primitive ideals of  $\mathcal C_q [SL_2]$, the quantum coordinate algebra of $SL_2$. Attached to each primitive ideal, we construct an irreducible $\mathcal C_q [SL_2]$-module study the tensor product of these modules. 

姜翠波：Simplicity rationality of moonshine type vertex operator algebras generated by Ising vectors of $\sigma$-type

Abstract: We prove  that a moonshine-type vertex operator algebra generated by Ising vectors of $\sigma$-type  associated to a 3-transposition group of symlectic typr given by Matsuo is simple, rational $C_2$-cofinite.  Together with the results of [Jiang-Lam-Yamauchi, 2017] , [Lam-Sakuma-Yamauchi, 2007], and  [ Matsuo, 2005], we give  a full  characterization of  this class of moonshine-type  vertex operator algebras. This is a joint work with Chinghung Lam Hiroshi Yamauchi.