QUOTIENT TRIANGULATED CATEGORIES ARISING IN REPRESENTATIONS OF ALGEBRAS

Abstract. Several kinds of quotient triangulated categories arising naturally in representations of algebras are studied; their relations with the stable categories of Frobenius exact categories are investigated; the derived categories of Gorenstein algebras are explicitly computed inside the stable categories of the graded module categories of the corresponding trivial extension algebras; new descriptions of the singularity categories of Gorenstein algebras are obtained. 1