Geodesic
SPECIAL TILTING MODULES FOR ALGEBRAS WITH POSITIVE DOMINANT DIMENSION
Glasgow mathematical journal, Tome 64 (2022) no. 1, pp. 79-105

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DOI

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 less than or equal to 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. 
PRESSLAND, MATTHEW; SAUTER, JULIA. SPECIAL TILTING MODULES FOR ALGEBRAS WITH POSITIVE DOMINANT DIMENSION. Glasgow mathematical journal, Tome 64 (2022) no. 1, pp. 79-105. doi: 10.1017/S0017089520000609
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     title = {SPECIAL {TILTING} {MODULES} {FOR} {ALGEBRAS} {WITH} {POSITIVE} {DOMINANT} {DIMENSION}},
     journal = {Glasgow mathematical journal},
     pages = {79--105},
     year = {2022},
     volume = {64},
     number = {1},
     doi = {10.1017/S0017089520000609},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089520000609/}
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