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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Abstract
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 |
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Status: | Published |
Refereed: | Yes |
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: | 0017-0895 |
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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