We study which algebras have tilting modules that are both generated and cogenerated by
projective–injective modules. Crawley–Boevey and Sauter have shown that Auslander …

A new homological symmetry condition is exhibited that extends and unifies several recently
defined and widely used concepts. Applications include general constructions of tilting …

For a finite-dimensional algebra Λ and a nonnegative integer n, we characterize when the
set tilt n Λ of additive equivalence classes of tilting modules with projective dimension at …

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 …

Tachikawa's second conjecture predicts that a finitely generated, orthogonal module over a
finite-dimensional self-injective algebra is projective. This conjecture is an important part of …

A new homological dimension, called rigidity dimension, is introduced to measure the
quality of resolutions of finite dimensional algebras (especially of infinite global dimension) …

We establish relations between Frobenius parts and between flat-dominant dimensions of
algebras linked by Frobenius bimodules. This is motivated by the Nakayama conjecture and …

Unlike Hochschild (co) homology and K-theory, global and dominant dimensions of
algebras are far from being invariant under derived equivalences in general. We show that …

Gendo-symmetric algebras were introduced by Fang and Koenig (Trans. Amer. Math. Soc.,
7: 5037–5055, 2016) as a generalisation of symmetric algebras. Namely, they are …

Derived categories and equivalences between them are the pièce de résistance of modern
homological algebra. They are widely used in many branches of mathematics, especially in …