On relative Auslander algebras

Asadollahi, Javad; Hafezi, Rasool

doi:10.1090/proc/14976

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On relative Auslander algebras

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

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https://doi.org/10.1090/proc/14976
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1711.07043.pdf
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Citation

Asadollahi, J., & Hafezi, R. (2020). On relative Auslander algebras. Proceedings of the American Mathematical Society, 148(6), 2379-2396. doi:10.1090/proc/14976.

Cite as: https://hdl.handle.net/21.11116/0000-0006-7B81-E

Abstract

Relative Auslander algebras were introduced and studied by Beligiannis. In this paper, we apply intermediate extension functors associated to certain recollements of functor categories to study them. In particular, we study the
existence of tilting-cotilting modules over such algebras. As a consequence, it will be shown that two Gorenstein algebras of G-dimension 1 being of finite Cohen-Macaulay type are Morita equivalent if and only if their Cohen-Macaulay
Auslander algebras are Morita equivalent.