乘法李共形代数及其共形模理论的研究

本项目主要研究乘法李共形代数及其共形模理论，研究内容主要分成如下三个方面：(1)研究乘法李共形代数的结构理论，包括泛中心扩张、共形导子、半单乘法李共形代数的直和分解等；(2)研究乘法李共形代数的有限不可约共形模的分类，以及不可约共形模之间扩张的分类问题；(3)研究乘法李共形代数的上同调理论，计算流乘法李共形代数和一般乘法李共形代数的上同调. 2023年7月在上海大学举办主题为“乘法李共形代数及相关领域”的高级研讨班，为期2周左右，规模约15人.

In this project, we mainly study multiplicative Lie conformal algebras and their conformal modules theory. The content can be divided into the following three parts: (1)We will study the structure theory of multiplicative Lie conformal algebras, including universal central extensions, conformal derivations, direct sum decomposition of semi-simple multiplicative Lie conformal algebras, etc.; (2)We shall study the classification of finite irreducible conformal modules of multiplicative Lie conformal algebras and the classification of extensions between irreducible conformal modules; (3)We will study the cohomology theory of multiplicative Lie conformal algebras and calculate the cohomology of current multiplicative Lie conformal algebras and general multiplicative Lie conformal algebras. In July 2023, we will hold an advanced seminar with the theme of "Multiplicative Lie conformal algebra and related topics" at Shanghai University for about two weeks, and 15 experts will be invited.