Hochschild Homology Of Some Algebras And Deformation Theory Of Split Algebras

The investigation of Hochschild cohomology and homology originated from the literature by G.Hochschild in 1945. C.C.Xi researched the Hochschild cohomology of algebras with homological ideals in 2000 and proved that, if Φ : A→B is a homological epimorphism, Hi(A) and Hi(B) can be connected with a long exact sequence. In this paper, Firstly, we researched the Hochschild homology of algebras with heredity ideals. The main conclusion is as follows: for i > 2, the Hochschild homology Hi(A) of an algebra A is equal to the the Hochschild homology Hi(B) of the algebra B where B = A/J and J is a heredity ideal of A.C.Cibils studied the Hochschild cohomology of split algebras with bicom-plexs. So, secondly, we constructed the one paremeter family of deformation of split algebras, we obtained the results from the method of C.Cibils, not from the definition given by M.Gerstenhaber. Specially, we discussed the one parameter family of deformation of trivial algebras.