An Auslander-Buchsbaum formula for higher Auslander algebras and applications
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866910835856637952 |
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| author | Cruz, Tiago Marczinzik, René |
| author_facet | Cruz, Tiago Marczinzik, René |
| contents | We provide a new non-commutative generalisation of the Auslander-Buchsbaum formula for higher Auslander algebras and use this to show that the class of tilted Auslander algebras, studied recently by Zito, and QF-1 algebras of global dimension at most 2, studied by Ringel in the 1970s, coincide. We furthermore give an explicit classification of this class of algebras and present generalisations to higher homological dimensions with a new local characterisation of QF-1 higher Auslander algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_08422 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Auslander-Buchsbaum formula for higher Auslander algebras and applications Cruz, Tiago Marczinzik, René Representation Theory Rings and Algebras 16G10 (Primary) 16E10, 16E65, 16S50, 16S90 (Secondary) We provide a new non-commutative generalisation of the Auslander-Buchsbaum formula for higher Auslander algebras and use this to show that the class of tilted Auslander algebras, studied recently by Zito, and QF-1 algebras of global dimension at most 2, studied by Ringel in the 1970s, coincide. We furthermore give an explicit classification of this class of algebras and present generalisations to higher homological dimensions with a new local characterisation of QF-1 higher Auslander algebras. |
| title | An Auslander-Buchsbaum formula for higher Auslander algebras and applications |
| topic | Representation Theory Rings and Algebras 16G10 (Primary) 16E10, 16E65, 16S50, 16S90 (Secondary) |
| url | https://arxiv.org/abs/2502.08422 |