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arXiv · 1705.03367

Special tilting modules for algebras with positive dominant dimension

Matthew Pressland·Julia Sauter
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Abstract

We study certain special tilting and cotilting modules for an algebra with positive dominant dimension, each of which is 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 minimal d-Auslander-Gorenstein algebras and d-Auslander algebras via the property that these special 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.

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BibTeXRIS

Matthew Pressland, Julia Sauter. 2021-01-12. Special tilting modules for algebras with positive dominant dimension. https://doi.org/10.1017/s0017089520000609

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