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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2107.07474 |
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| _version_ | 1866909723718057984 |
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| author | Kirkman, Ellen Won, Robert Zhang, James J. |
| author_facet | Kirkman, Ellen Won, Robert Zhang, James J. |
| contents | This paper concerns homological notions of regularity for noncommutative algebras. Properties of an algebra $A$ are reflected in the regularities of certain (complexes of) $A$-modules. We study the classical Tor-regularity and Castelnuovo-Mumford regularity, which were generalized from the commutative setting to the noncommutative setting by Jørgensen and Dong-Wu. We also introduce two new numerical homological invariants: concavity and Artin-Schelter regularity. Artin-Schelter regular algebras occupy a central position in noncommutative algebra and noncommutative algebraic geometry, and we use these invariants to establish criteria which can be used to determine whether a noetherian connected graded algebra is Artin-Schelter regular. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_07474 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Homological regularities and concavities Kirkman, Ellen Won, Robert Zhang, James J. Rings and Algebras 16E10, 16E65, 20J99 This paper concerns homological notions of regularity for noncommutative algebras. Properties of an algebra $A$ are reflected in the regularities of certain (complexes of) $A$-modules. We study the classical Tor-regularity and Castelnuovo-Mumford regularity, which were generalized from the commutative setting to the noncommutative setting by Jørgensen and Dong-Wu. We also introduce two new numerical homological invariants: concavity and Artin-Schelter regularity. Artin-Schelter regular algebras occupy a central position in noncommutative algebra and noncommutative algebraic geometry, and we use these invariants to establish criteria which can be used to determine whether a noetherian connected graded algebra is Artin-Schelter regular. |
| title | Homological regularities and concavities |
| topic | Rings and Algebras 16E10, 16E65, 20J99 |
| url | https://arxiv.org/abs/2107.07474 |