摘要
对高维丛范畴中丛倾斜对象的存在性及其性质进行了研究,讨论了有限型d-丛范畴中存在丛倾斜对象满足它的自同态代数为自入射代数的情形.证明了:(1)当d>1时,d-丛范畴的几乎完备丛倾斜对象只有一个补;(2)d-丛范畴的丛倾斜对象都是由遗传代数上的倾斜模诱导的,并给出了倾斜模诱导d-丛范畴的丛倾斜对象的一个充分条件;(3)对于有限型d-丛范畴,有限型3-丛范畴存在丛倾斜对象当且仅当3-丛范畴是A_1,A_3.D_(2n-1)(n>2)型的;(4)D_(2n-1)型(2m+1)-丛范畴存在一个丛倾斜对象满足其自同态代数为自入射代数,且其模范畴的稳定范畴等价于A_(4mn-4m+2n-1)型(4m+2)-丛范畴.
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 or D2n-1 （n）, 2）. （4） The （2rn ＋ 1）-cluster category of type D2n-1 admits a cluster-tilting object such that its endomorphism algebra is seif-Injective, and its stable category is equivalent to the （4m ＋ 2）-cluster category of type A4mn-4m＋2n-1.
出处
《数学进展》
CSCD
北大核心
2016年第5期641-651,共11页
Advances in Mathematics（China）
基金
国家自然科学基金(No.11401401)
中央高校基本科研业务费专项资金(No.A0920502051411-45)
