Let A be a basic connected finite dimensional associative algebra over an algebraically closed field k and G be a cyclic group.There is a quiver QGwith relationsρG such that the skew group algebras A[G]is Morita equi...Let A be a basic connected finite dimensional associative algebra over an algebraically closed field k and G be a cyclic group.There is a quiver QGwith relationsρG such that the skew group algebras A[G]is Morita equivalent to the quotient algebra of path algebra kQGmodulo ideal(ρG).Generally,the quiver QGis not connected.In this paper we develop a method to determine the number of connect components of QG.Meanwhile,we introduce the notion of weight for underlying quiver of A such that A is G-graded and determine the connect components of smash product A#kG*.展开更多
The present paper focuses on the study of the stable category of vector bundles for the weighted projective lines of weight triple. We find some important triangles in this category and use them to construct tilting o...The present paper focuses on the study of the stable category of vector bundles for the weighted projective lines of weight triple. We find some important triangles in this category and use them to construct tilting objects with tubular endomorphism algebras for the case of genus one via cluster tilting theory.展开更多
In the present paper, we introduce the concepts of Prüfer sheaves and adic sheaves over a weighted projective line of genus one or an elliptic curve, show that Prüfer sheaves and adic sheaves can characteriz...In the present paper, we introduce the concepts of Prüfer sheaves and adic sheaves over a weighted projective line of genus one or an elliptic curve, show that Prüfer sheaves and adic sheaves can characterize the category of coherent sheaves. Moreover, we describe the relationship between Prüfer sheaves and generic sheaves, and provide two methods to construct generic sheaves by using coherent sheaves and Prüfer sheaves.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.11871404,11971398 and 12131018)。
文摘Let A be a basic connected finite dimensional associative algebra over an algebraically closed field k and G be a cyclic group.There is a quiver QGwith relationsρG such that the skew group algebras A[G]is Morita equivalent to the quotient algebra of path algebra kQGmodulo ideal(ρG).Generally,the quiver QGis not connected.In this paper we develop a method to determine the number of connect components of QG.Meanwhile,we introduce the notion of weight for underlying quiver of A such that A is G-graded and determine the connect components of smash product A#kG*.
基金Partially supported by the National Natural Science Foundation of China(Grant Nos.11571286,11871404and 11801473)the Natural Science Foundation of Fujian Province of China(Grant No.2016J01031)the Fundamental Research Funds for the Central Universities of China(Grant Nos.20720180002 and 20720180006)
文摘The present paper focuses on the study of the stable category of vector bundles for the weighted projective lines of weight triple. We find some important triangles in this category and use them to construct tilting objects with tubular endomorphism algebras for the case of genus one via cluster tilting theory.
基金Supported by National Nature Science Foundation of China(Grant Nos.11571286,11471269)the Natural Science Foundation of Fujian Province of China(Grant No.2016J01031)the Fundamental Research Funds for the Central Universities of China(Grant No.20720150006)
文摘In the present paper, we introduce the concepts of Prüfer sheaves and adic sheaves over a weighted projective line of genus one or an elliptic curve, show that Prüfer sheaves and adic sheaves can characterize the category of coherent sheaves. Moreover, we describe the relationship between Prüfer sheaves and generic sheaves, and provide two methods to construct generic sheaves by using coherent sheaves and Prüfer sheaves.
