map代数的不可约表示

设g是一个李（共形，超）代数，A是一个含单位元的交换结合代数，那么在g与A的张量积上可以自然地定义一个李（共形，超）代数结构，这样得到的代数称为map李（共形，超）代数。这是李理论中构造新代数的一个十分有效的方法。. 在本项目中，我们将研究这样得到的一些map李（共形，超）代数的表示问题。特别地，我们想对它们的满足某些有限性条件的不可约模给出一个分类。例如，我们想解决当g是一个有限单李共形代数，而A是一个有限生成代数时，对应代数的有限不可约模的分类问题。以及当g是一个A型的李超代数，A是一个有限生成代数时，对应代数的不可约容许模的分类问题。

Assume that g is a Lie (conformal, super) algebra and A is a commutative associative algebra with unity. Then there exists a natural structure of Lie (conformal, super) algebra on the tensor product of g and A. An algebra obtained in this way is called a map Lie (conformal, super) algebra. This is a very efficient method to construct new algebras in Lie theory.. In this project, we will study the representations of certain map Lie (conformal, super) algebras. Especially, we aim to give a classificaiton of the irreducible modules satisfying some finite properties. For example, we want to give a classification of finite irreducible modules over the corresponding map Lie conformal algebra when g is a finite simple Lie conformal algebra and A is a finitely generated algebra. We also want to give a classification of irreducible admissible modules over the corresponding map Lie superalgebra provided g is a finite simple Lie superalgebra of type A and A is a finitely generated algebra.