Auslander's Formula for contravariantly finite subcategories

Asadollahi, Javad; Hafezi, Rasool; Keshavarz, Mohammad H.

doi:10.2969/jmsj/83308330

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Auslander's Formula for contravariantly finite subcategories

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Asadollahi, Javad
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.2969/jmsj/83308330
(Publisher version)

https://doi.org/10.48550/arXiv.1701.00073
(Preprint)

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Citation

Asadollahi, J., Hafezi, R., & Keshavarz, M. H. (2021). Auslander's Formula for contravariantly finite subcategories. Journal of the Mathematical Society of Japan, 73(2), 329-349. doi:10.2969/jmsj/83308330.

Cite as: https://hdl.handle.net/21.11116/0000-0008-F4BE-F

Abstract

A relative version of Auslander's formula with respect to a contravariantly finite subcategory will be given. Dual version will be treated. Several examples and applications will be provided. In particular, we show that under
certain circumstances, if relative Auslander algebras of artin algebras
$\Lambda$ and $\Lambda'$ are Morita equivalent, then $\Lambda$ and $\Lambda'$
are also Morita equivalent.