Representation theory of partial relation extensions
Representation theory of partial relation extensions
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部分关系扩展的表示论
DOI：
10.4064/cm7511-3-2018
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发表时间：
2016
影响因子：
0.4
通讯作者：
D. Smith
中科院分区：
文献类型：
--
作者：
I. Assem;J. C. Bustamante;Julie Dionne;P. Meur;D. Smith
设C是一个全局维数不超过2的有限维代数。偏关系扩展是C通过其关系C-C-双模的直接和的任何平凡扩展。当C是倾斜代数时，这种构造提供了倾斜代数和簇倾斜代数之间的中间代数。本文研究了部分关系扩展的表示理论。当C倾斜时，C的Auslander-Reiten颤振中的任何完整切片作为局部切片嵌入到部分关系扩展的Auslander-Reiten颤振中；此外，通过考虑由C的最小关系系统产生的势的直接和分解，介绍了产生部分关系扩展的系统方法。
Let C be a finite dimensional algebra of global dimension at most two. A partial relation extension is any trivial extension of C by a direct summand of its relation C-C-bimodule. When C is a tilted algebra, this construction provides an intermediate class of algebras between tilted and cluster tilted algebras. The text investigates the representation theory of partial relation extensions. When C is tilted, any complete slice in the Auslander-Reiten quiver of C embeds as a local slice in the Auslander-Reiten quiver of the partial relation extension; Moreover, a systematic way of producing partial relation extensions is introduced by considering direct sum decompositions of the potential arising from a minimal system of relations of C.