Endomorphism algebras for a class of negative Calabi-Yau categories
Endomorphism algebras for a class of negative Calabi-Yau categories
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一类负 Calabi-Yau 范畴的自同态代数
DOI：
10.1016/j.jalgebra.2017.07.016
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
M. J. Parsons
中科院分区：
文献类型：
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作者：
Raquel Coelho Guardado Simões;M. J. Parsons
我们考虑 A n 型路径代数的有界派生范畴的轨道范畴，对于 m⩾ 1，它可以被视为 a−(m+ 1)-簇范畴。特别地，我们给出了那些自同态代数相连的最大 m 刚性对象的表征，然后用它来显式地研究这些代数。具体来说，我们从箭袋和关系方面对它们进行了完整的描述，并将它们与 A 型的（更高）簇倾斜代数联系起来。作为副产品，我们引入了一类更大的代数，称为平铺代数。
We consider an orbit category of the bounded derived category of a path algebra of type A n which can be viewed as a−(m+ 1)-cluster category, for m⩾ 1. In particular, we give a characterisation of those maximal m-rigid objects whose endomorphism algebras are connected, and then use it to explicitly study these algebras. Specifically, we give a full description of them in terms of quivers and relations, and relate them with (higher) cluster-tilted algebras of type A. As a by-product, we introduce a larger class of algebras, called tiling algebras.