图代数作为代数学中重要的研究对象，在统计力学、量子场论以及扭结理论中有着很强的理论及应用价值。而图代数塔的Grothendieck群上往往有丰富的代数结构，因此是实现经典代数范畴化的有力工具。本项目考虑某些与Schur-Weyl对偶理论所紧密联系的图代数塔，如Temperley-Lieb、Brauer以及partition代数塔等。一方面，试图通过研究代数塔的表示与同调方面的性质来确定其Grothendieck群上的代数结构，包括结合代数结构、余代数及Hopf代数结构。另一方面，研究用公理化方式定义的图代数塔的Grothendieck群。

Diagram algebras, as an important class of study objects in algebra, have great theoretical and practical importance in statistical mechanics, quantum field theory and knot theory. Lots of towers of diagram algebras have rich algebraic structures on their Grothendieck groups. Hence, the framework of towers is a powerful tool in realizing the categorification of classical algebras. This project emphasizes the towers of diagram algebras which are closely related to the theory of Schur-Weyl duality, such as the towers of the Temperley-Lieb algebras, Brauer algebras and partition algebras. We will investigate the algebraic structures on the Grothendieck groups of the towers of algebras by studying the representations and homologies, involving the structures of associative algebra, coalgebra and Hopf algebra. Moreover, we will study the Grothendieck groups of the towers defined by an axiomatic manner.