Rigidity dimension of algebras
Rigidity dimension of algebras
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DOI：
10.1017/s0305004119000513
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发表时间：
2019-11
影响因子：
0.8
通讯作者：
Hongxing Chen;M. Fang;O. Kerner;S. Koenig;K. Yamagata
中科院分区：
文献类型：
--
作者：
Hongxing Chen;M. Fang;O. Kerner;S. Koenig;K. Yamagata
摘要引入了一种新的同调维度，称为刚性维度，用来衡量有限维代数(特别是无限整体维代数)在有限整体维代数和大优势维代数上的分解质量。根据扩张和Hochschild上同调建立了维数的上界，而有限一般是由同调猜想得到的。特别地，非半单群代数的刚性维度是有限的，并且由群的阶有界。然后证明了在稳定等价下的不变性是成立的，除了在加性等价情况下有节点时的一些例外，在三角等价的情况下没有例外。证明了自内射代数之间的Morita型等价和派生等价的稳定等价也保持了刚性维.
Abstract A new homological dimension, called rigidity dimension, is introduced to measure the quality of resolutions of finite dimensional algebras (especially of infinite global dimension) by algebras of finite global dimension and big dominant dimension. Upper bounds of the dimension are established in terms of extensions and of Hochschild cohomology, and finiteness in general is derived from homological conjectures. In particular, the rigidity dimension of a non-semisimple group algebra is finite and bounded by the order of the group. Then invariance under stable equivalences is shown to hold, with some exceptions when there are nodes in case of additive equivalences, and without exceptions in case of triangulated equivalences. Stable equivalences of Morita type and derived equivalences, both between self-injective algebras, are shown to preserve rigidity dimension as well.