Special tilting modules for algebras with positive dominant dimension

Pressland, M. and Sauter, J. (2022) Special tilting modules for algebras with positive dominant dimension. Glasgow Mathematical Journal, 64(1), pp. 79-105. (doi: 10.1017/S0017089520000609)

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We study a set of uniquely determined tilting and cotilting modules for an algebra with positive dominant dimension, with the property that they are generated or cogenerated (and usually both) by projective-injectives. These modules have various interesting properties, for example that their endomorphism algebras always have global dimension at most that of the original algebra. We characterise d-Auslander-Gorenstein algebras and d-Auslander algebras via the property that the relevant tilting and cotilting modules coincide. By the Morita-Tachikawa correspondence, any algebra of dominant dimension at least 2 may be expressed (essentially uniquely) as the endomorphism algebra of a generator-cogenerator for another algebra, and we also study our special tilting and cotilting modules from this point of view, via the theory of recollements and intermediate extension functors.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Pressland, Dr Matthew
Authors: Pressland, M., and Sauter, J.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Glasgow Mathematical Journal
Publisher:Cambridge University Press
ISSN (Online):1469-509X
Published Online:09 December 2020
Copyright Holders:Copyright © 2020 The Authors
First Published:First published in Glasgow Mathematical Journal 64(1): 79-105
Publisher Policy:Reproduced under a Creative Commons License

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