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arXiv · 2108.12923

Homological properties of extensions of algebras

Kostiantyn Iusenko·John W. MacQuarrie
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Abstract

We consider a class of extensions of associative algebras, which we refer to as ``strongly proj-bounded extensions''. We prove that the finiteness of the left global dimension and the support of the Hochschild homology is preserved by strongly proj-bounded extensions, generalizing results of Cibils, Lanzillota, Marcos and Solotar. Moreover, we show that the finiteness of the big left finitistic dimension is preserved by strongly proj-bounded extensions. In order to construct examples, we describe a new class of extensions of algebras of finite relative global dimension, which may be of independent interest. The results apply both for abstract (meaning no topology) and pseudocompact algebras.

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Kostiantyn Iusenko, John W. MacQuarrie. 2021-08-29. Homological properties of extensions of algebras. https://arxiv.org/abs/2108.12923

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