Using complexity,we can also study the structure of the A-R quiver of a group algebra. The selfinjective Koszul algebra of finite complexity is an important class of algebras,there is some nice relation between the stable category of such algebras with the derived category of coherent sheaves.
Similar to [KV2], for a Dynkin-algebra A, we prove that there is a bijection between the bi-aisles in Db(A) and thestrictly full triangulated subcategories of Db(A) which are closed under direct sum-mands.
The second part of this thesis is due to study the t-structures on the derived cat-egory of a negative dg category. We prove that for a negative dg category A, the derivedcategory D(A) has a natural t-structure defined by the homology groups.
The notion of derived categories (trangulated categories) was first introduced and studied by Grothendieck-Verdier in early sixties of last century, which marks a new starting point of the development of modern algebras. The theory of derived categories establish a beautiful relation between algebras and geometries.
In the first chapter, we give a detailed introduction of recent developments in derived categories, Morita's equivalence theory, derived equivalence (autoequivalence) theory, recollements and mutations, automorphisms of Lie algebras, and so on.