半群和半群代数在数学的许多重要分支都有广泛应用， 如拓扑、概率和组合等学科，也受到Fields奖获得者E.J.Zelmanov等著名人物的关注。本项目主要研究半群代数（特别是正则半群代数）的有限维数、仿射胞腔结构（包括胞腔链的长度、中心、根基和拟遗传性）、导出范畴粘合和Frobenius双模扩张等相关问题。有限维数猜想是阿丁代数表示论中的一个著名猜想，至今未解决；而仿射胞腔结构能为解决一类无限维代数的不可约表示参数化问题提供统一框架。因此对半群代数这些问题的研究将极大开拓和丰富半群代数的表示理论，并对有限维数猜想和仿射胞腔代数理论的深入发展产生积极的作用。

Semigroups and semigroup algebras are widely used in many important areas of mathematics, such as topology, probability and combinatorics, and have also attracted attentions of the Fields Medal winner E.J.Zelmanov and other international leading experts. This project mainly studies the finitistic dimension, affine cellular structure (including the length of cellular chains, center, radical and quasi-heredity), Frobenius bimodule extensions and related problems of semigroup algebras, specially regular semigroup algebras, and recollements of their derived module categories. The finitistic dimension conjecture, which is still open, is one of the most famous conjectures in the representation theory of Artin algebras; while affine cellular structure of algebras can provide a unified framework for parameterizing irreducible representations of a class of infinite-dimensional algebras. The implementation of this project will not only greatly enrich the research of the representation theory of semigroup algebras, but also have strongly positive influences on the deep development of the finististic dimension conjecture and affine cellular algebras.