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.

中文翻译：

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代数的刚性维数

引入了一种新的同调维数，称为刚性维数，用有限全局维数和大主维数的代数来衡量有限维代数（尤其是无限全局维数）的分辨率质量。维数的上限是根据外延和 Hochschild 上同调建立的，一般来说，有限性是从同调猜想推导出来的。特别是，非半单群代数的刚性维数是有限的并且受群阶的限制。那么稳定等价下的不变性被证明是成立的，除了在加法等价的情况下存在节点时有一些例外，在三角等价的情况下没有例外。Morita 类型的稳定等价和派生等价，都在自内射代数之间，