It is well known that Virasoro elements play an extremely important role in the theory of vertex operator algebras, and likewise a very significant role in the field of conformal algebras. In this talk, we introduce the notion of a regular action in the category of conformal modules over Lie conformal algebras with Virasoroelements. We show that a finite conformal module over the general conformal algebra of rank 1 (resp., rank N with N>1) is semisimple if and only if there exists a pair of different Virasoro elements (resp., canonical Virasoroelements) with regular actions. Along the way to finding a semisimplicity criteria, we also discuss the classification of Virasoro elements of general conformal algebras, leading us to construct a huge number of new Virasoro conformal modules. This is a joint work with Chunguang Xia.

苏育才，集美大学和同济大学特聘教授，博士生导师，2002年入选教育部跨世纪人才，2005年入选中国科学院百人计划，2008年荣获国家杰出青年科学基金，2012年入选上海市优秀学科带头人，2015年享受国务院政府特殊津贴。主要从事代数学中的李理论、数学物理中的共形场论、理论物理中的超对称性等方面的研究。先后主持国家自然科学重点基金、国家自然科学面上基金、上海市优秀学术带头人计划等省部级以上基金多项。任 Algebra Colloquium、数学学报杂志编委。在J.Eur.Math.Soc., Adv. Math., Comm. Math. Phys., Proc. London Math. Soc., Math. Z., Israel J.Math.等20多种国际期刊上发表论文100多篇。