Cluster-tilting objects in higher cluster categories  

作　　者：Xinhong CHEN Ming LU 

机构地区：[1]Department of Mathematics,Southwest Jiaotong University,Chengdu 610031,China [2]Department of Mathematics,Sichuan University,Chengdu 610064,China

出　　处：《Frontiers of Mathematics in China》2023年第3期187-201,共15页中国高等学校学术文摘·数学（英文）

摘　　要：We consider the existence of cluster-tilting objects in a d-cluster category such that its endomorphism algebra is self-injective,and also the properties for cluster-tilting objects in d-cluster categories.We get the following results:(1)When d>1,any almost complete cluster-tilting object in d-cluster category has only one complement.(2)Cluster-tilting objects in d-cluster categories are induced by tilting modules over some hereditary algebras.We also give a condition for a tilting module to induce a cluster-tilting object in a d-cluster category.(3)A 3-cluster category of finite type admits a cluster-tilting object if and only if its type is A1,A3,D2n-1(n>2).(4)The(2m+1)-cluster category of type D2n-1 admits a cluster-tilting object such that its endomorphism algebra is self-injective,and its stable category is equivalent to the(4m+2)-cluster category of type A4mn-4m+2n-1.

关 键 词：Almost complete cluster-tilting object Calabi-Yau 1 triangulated category cluster-tilting object COMPLEMENT d-cluster category 

分 类 号：O15[理学—数学]