Homological properties of extensions of algebras
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866909448092516352 |
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| author | Iusenko, Kostiantyn MacQuarrie, John W. |
| author_facet | Iusenko, Kostiantyn MacQuarrie, John W. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_12923 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Homological properties of extensions of algebras Iusenko, Kostiantyn MacQuarrie, John W. K-Theory and Homology Rings and Algebras Representation Theory 18G25, 16E40, 16E30, 16W80, 18A30 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. |
| title | Homological properties of extensions of algebras |
| topic | K-Theory and Homology Rings and Algebras Representation Theory 18G25, 16E40, 16E30, 16W80, 18A30 |
| url | https://arxiv.org/abs/2108.12923 |