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arXiv · 2502.08422

An Auslander-Buchsbaum formula for higher Auslander algebras and applications

Tiago Cruz·René Marczinzik
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Abstract

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.

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Tiago Cruz, René Marczinzik. 2025-02-12. An Auslander-Buchsbaum formula for higher Auslander algebras and applications. https://arxiv.org/abs/2502.08422

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