Title: Special tilting modules for algebras with positive dominant dimension,
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.