关于Gorenstein代数上的Hall代数的研究

The project is devoted to the research of Hall algebras over Gorenstein algebras through the theory of Gorenstein homological algebra. A series of problems related to Bridgeland's Hall algebras of 2-periodic complexes over Gorenstein algebras will be investigated, and Hall algebras over cluster-tilted algebras will be studied. The expected achievements will provide new ideas and methods to cluster-tilting theory and Hall algebras over algebras of infinite global dimension.

本项目旨在利用Gorenstein同调代数理论对Gorenstein代数上的Hall代数进行研究。将探索Gorenstein代数上2-周期复形范畴在Bridgeland意义下的Hall代数相关的一系列问题，并具体研究丛倾斜代数上的Hall代数。其结果将为整体维数无限的代数上的Hall代数和丛倾斜理论提供新的理论和方法。