scholarly journals On self-injective algebras of stable dimension zero

2011 ◽  
Vol 203 ◽  
pp. 101-108 ◽  
Author(s):  
Michio Yoshiwaki
Keyword(s):  
Module Category ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
Stable Module Category ◽  
Dimension Zero ◽  
Stable Dimension ◽  
Stable Module

AbstractLet A be a self-injective algebra over an algebraically closed field. We study the stable dimension of A, which is the dimension of the stable module category of A in the sense of Rouquier. Then we prove that A is representation-finite if the stable dimension of A is zero.

scholarly journals On self-injective algebras of stable dimension zero

2011 ◽  
Vol 203 ◽  
pp. 101-108
Author(s):  
Michio Yoshiwaki
Keyword(s):  
Module Category ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
Stable Module Category ◽  
Dimension Zero ◽  
Stable Dimension ◽  
Stable Module

AbstractLetAbe a self-injective algebra over an algebraically closed field. We study the stable dimension ofA, which is the dimension of the stable module category ofAin the sense of Rouquier. Then we prove thatAis representation-finite if the stable dimension ofAis zero.

scholarly journals THE GRADED CENTER OF A TRIANGULATED CATEGORY

2016 ◽  
Vol 102 (1) ◽  
pp. 74-95
Author(s):  
JON F. CARLSON ◽  
PETER WEBB
Keyword(s):  
Group Algebra ◽  
Special Kind ◽  
Module Category ◽  
Triangulated Category ◽  
Triangulated Categories ◽  
Stable Module Category ◽  
Natural Transformations ◽  
Stable Module ◽  
Serre Functor

With applications in mind to the representations and cohomology of block algebras, we examine elements of the graded center of a triangulated category when the category has a Serre functor. These are natural transformations from the identity functor to powers of the shift functor that commute with the shift functor. We show that such natural transformations that have support in a single shift orbit of indecomposable objects are necessarily of a kind previously constructed by Linckelmann. Under further conditions, when the support is contained in only finitely many shift orbits, sums of transformations of this special kind account for all possibilities. Allowing infinitely many shift orbits in the support, we construct elements of the graded center of the stable module category of a tame group algebra of a kind that cannot occur with wild block algebras. We use functorial methods extensively in the proof, developing some of this theory in the context of triangulated categories.

scholarly journals Recollement of homotopy categories and Cohen-Macaulay modules

2011 ◽  
Vol 8 (3) ◽  
pp. 507-542 ◽  
Author(s):  
Osamu Iyama ◽  
Kiriko Kato ◽  
Jun-ichi Miyachi
Keyword(s):  
Homotopy Category ◽  
Module Category ◽  
Gorenstein Ring ◽  
Projective Modules ◽  
Finitely Generated ◽  
Stable Module Category ◽  
Quotient Category ◽  
Stable Module

AbstractWe study the homotopy category of unbounded complexes with bounded homologies and its quotient category by the homotopy category of bounded complexes. In the case of the homotopy category of finitely generated projective modules over an Iwanaga-Gorenstein ring, we show the existence of a new structure in the above quotient category, which we call a triangle of recollements. Moreover, we show that this quotient category is triangle equivalent to the stable module category of Cohen-Macaulay T2(R)-modules.

scholarly journals The generating hypothesis for the stable module category of a p-group

2007 ◽  
Vol 310 (1) ◽  
pp. 428-433 ◽  
Author(s):  
David J. Benson ◽  
Sunil K. Chebolu ◽  
J. Daniel Christensen ◽  
Ján Mináč
Keyword(s):  
Module Category ◽  
Stable Module Category ◽  
Stable Module ◽  
Generating Hypothesis

scholarly journals Phantom Maps in the Stable Module Category

1998 ◽  
Vol 201 (2) ◽  
pp. 686-702 ◽  
Author(s):  
Gilles Ph Gnacadja
Keyword(s):  
Module Category ◽  
Stable Module Category ◽  
Phantom Maps ◽  
Stable Module
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