广义路代数及其Hochschild上同调  

Generalized Path Algebras and Their Hochschild Cohomology

作　　者：姚海楼[1] 周丽丽[1] 

机构地区：[1]北京工业大学应用数理学院,北京100124

出　　处：《北京工业大学学报》2016年第4期628-631,640,共5页Journal of Beijing University of Technology

基　　金：国家自然科学基金资助项目(11271119);北京市自然科学基金资助项目(1122002)

摘　　要：为了研究quiverΔ上的A-广义路代数R=k(Δ,A),基于本原正交幂等元完全集,给出了广义路代数R=k(Δ,A)的不可分解投射模与内射模以及单模的构造形式.基于遗传代数性质得到了广义路代数是遗传代数的充要条件,并进一步在同调理论和有限维代数的Hochschild上同调的基础上得到了广义路代数的Hochschild上同调.To study a generalized path algebra on the quiver△, all its indecomposable projective modules and injective modules, and simple modules were constructed by using a complete set of its orthogonal primitive elements. Based on the properties of hereditary algebras a sufficient and necessary condition for a generalized path algebra R =k(△,A) to be hereditary was proposed. Furthermore, the Hochschild cohomology of R = k (△, A ) based on homology theory and Hochschild cohomology of a finitely dimensional algebra was obtained.

关 键 词：广义路代数 HOCHSCHILD上同调 遗传代数 

分 类 号：O153.3[理学—数学]