(Ebook) Realizing stable categories as derived categories by K Yamaura ISBN 9780273693581, 9781405871778, 0273693581, 1405871776

(Ebook) Realizing stable categories as derived categories by K Yamaura ISBN 9780273693581, 9781405871778, 0273693581, 1405871776

In this paper, we discuss a relationship between representation theory of graded self-injective algebras and that of algebras of finite global dimension. For a positively graded self-injective algebra A such that A"0 has finite global dimension, we construct two types of triangle-equivalences. First we show that there exists a triangle-equivalence between the stable category of Z-graded A-modules and the derived category of a certain algebra @C of finite global dimension. Secondly we show that if A has Gorenstein parameter @?, then there exists a triangle-equivalence between the stable category of Z/@?Z-graded A-modules and a derived-orbit category of @C, which is a triangulated hull of the orbit category of the derived category.Abstract: In this paper, we discuss a relationship between representation theory of graded self-injective algebras and that of algebras of finite global dimension. For a positively graded self-injective algebra A such that A"0 has finite global dimension, we construct two types of triangle-equivalences. First we show that there exists a triangle-equivalence between the stable category of Z-graded A-modules and the derived category of a certain algebra @C of finite global dimension. Secondly we show that if A has Gorenstein parameter @?, then there exists a triangle-equivalence between the stable category of Z/@?Z-graded A-modules and a derived-orbit category of @C, which is a triangulated hull of the orbit category of the derived category