On Exceptional Sequences Over Finite Dimensional Hereditary Algebras

The notation of exceptional sequence came from the study of vector bundles. In 1993,W.Crawley-Boevey introduced the conception of exceptional sequence to the representation theory of path algebra.He has shown that the braid group acts transitively on the set of complete exceptional sequence. In 1994,C.M.Ringel presented a direct proof,which is valid for an arbitrary Artin algebra. In recent years,the endomorphism algebras of complete exceptional sequence of type An and An have been researched. Furthermore,the inductive formula of the number of complete exceptional sequence over hereditary algebras of finite representation type has been obtained.Perpendicular category plays an important role in the study of exceptional sequence. In chapter l,some fundamental notations,which will be used in the article,and the backgrounds,are given. In chapter 2, we get some conclusions for the completion of the almost complete exceptional sequence of representation-finite type algebra and finite dimensional algebra using perpendicular category. In chapter 3,we study the property of complete exceptional sequence. In chapter 4,we make research on the Hochschild cohomology of endomorphism algebras of complete exceptional sequence over hereditary algebras. Especially,we compute the Hochschild cohomology of endomorphism algebras of complete exceptional sequence of the path algebra whose quiver has 3 vertices and has no orientation.