Generalized Path Algebras And Their Hochschild Cohomology

In this thesis we dicuss the category RepR of representations of generalized path algebras ,Hochschild cohomology of generalized path algebras, Hochschild cohomology of quotients of generalized path algebras.This paper consists of the following contents:In chapter 1 we give some notations,basic concepts,researching background and the main results.In chapter 2 we prove that the category RepR of representations of generalized path algebras and the category f.d.R of fintely generated R-modules are equivalent,we also give some examples of projective representations,injective representations,simple representations of generalized path algebras.In chapter 3 we dicuss the hereditary of generalized path algebras,generalized path algebras R=k(â–³,(?))is hereditary if and only if for eachi∈△₀,A_i is hereditary. In chapter 4 if R is hereditary,we get H⁰(R)= k;dim_kH^R=l-dim_k(?)+(?)Ï…(a), whereÏ…(α)=dim_kA_s(α)RA_e(α);H^m(R)=0,m≥2.In chapter 5 we mainly dicuss Hochschild cohomoloy of radical square zero algebras and Hochschild cohomoloy of incidence algebras.