Let A be an Artin algebra.We investigate subalgebras of A with certain conditions and obtain some classes of algebras whose finitistic dimensions are finite.
The main objective of this paper is to study the dimension trees and further the homological dimensions of the extension algebras -- dual and trivially twisted extensions -- with a unified combinatorial approach using...The main objective of this paper is to study the dimension trees and further the homological dimensions of the extension algebras -- dual and trivially twisted extensions -- with a unified combinatorial approach using the two combinatorial algorithms -- Topdown and Bottomup. We first present a more complete and clearer picture of a dimension tree, with which we are then able, on the one hand, to sharpen some results obtained before and furthermore reveal a few more hidden subtle homological phenomenons of or connections between the involved algebras; on the other hand, to provide two more efficient combinatorial algorithms for computing dimension trees, and consequently the homological dimensions as an application. We believe that the more refined complete structural information on dimension trees will be useful to study other homological properties of this class of extension algebras.展开更多
We generalize the concept -- dimension tree and the related results for monomial algebras to a more general case -- relations algebras A by bringing GrSbner basis into play. More precisely, we will describe the minima...We generalize the concept -- dimension tree and the related results for monomial algebras to a more general case -- relations algebras A by bringing GrSbner basis into play. More precisely, we will describe the minimal projective resolution of a left A-module M as a rooted ＇weighted＇ diagraph to be called the minimal resolution graph for M. Algorithms for computing such diagraphs and applications as well will be presented.展开更多
By using the stable t-structure induced by an adjoint pair, we extend several results con- cerning recollements to upper （resp. lower） recollements. These include the fundamental results of Par-shall and Scott on co...By using the stable t-structure induced by an adjoint pair, we extend several results con- cerning recollements to upper （resp. lower） recollements. These include the fundamental results of Par-shall and Scott on comparisons of recollements, Wiedemann＇s result on the global dimension and Hap- pel＇s result on the finitistic dimension, occurring in a recollement （Db（A＇）, Db（A）, Db（A＂）） of bounded derived categories of Artin algebras. We introduce and describe a triangle expansion of a triangulated category and illustrate it by examples.展开更多
基金Supported by the NSFC (10771112)NSF of Shandong Province (Y2008A05)
文摘Let A be an Artin algebra.We investigate subalgebras of A with certain conditions and obtain some classes of algebras whose finitistic dimensions are finite.
基金Supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD)
文摘The main objective of this paper is to study the dimension trees and further the homological dimensions of the extension algebras -- dual and trivially twisted extensions -- with a unified combinatorial approach using the two combinatorial algorithms -- Topdown and Bottomup. We first present a more complete and clearer picture of a dimension tree, with which we are then able, on the one hand, to sharpen some results obtained before and furthermore reveal a few more hidden subtle homological phenomenons of or connections between the involved algebras; on the other hand, to provide two more efficient combinatorial algorithms for computing dimension trees, and consequently the homological dimensions as an application. We believe that the more refined complete structural information on dimension trees will be useful to study other homological properties of this class of extension algebras.
文摘We generalize the concept -- dimension tree and the related results for monomial algebras to a more general case -- relations algebras A by bringing GrSbner basis into play. More precisely, we will describe the minimal projective resolution of a left A-module M as a rooted ＇weighted＇ diagraph to be called the minimal resolution graph for M. Algorithms for computing such diagraphs and applications as well will be presented.
基金Supported by National Natural Science Foundation of China(Grant Nos.11271251,11431010 and 11571239)
文摘By using the stable t-structure induced by an adjoint pair, we extend several results con- cerning recollements to upper （resp. lower） recollements. These include the fundamental results of Par-shall and Scott on comparisons of recollements, Wiedemann＇s result on the global dimension and Hap- pel＇s result on the finitistic dimension, occurring in a recollement （Db（A＇）, Db（A）, Db（A＂）） of bounded derived categories of Artin algebras. We introduce and describe a triangle expansion of a triangulated category and illustrate it by examples.
