Important connections in representation theory arise from resolving a finite-dimensional
algebra by an endomorphism algebra of a generator-cogenerator with finite global …

Important correspondences in representation theory can be regarded as restrictions of the
Morita--Tachikawa correspondence. Moreover, this correspondence motivates the study of …

The category of all additive functors Mod (modΛ) for a finite dimensional algebra Λ were
shown to be left Noetherian if and only if Λ is of finite representation type by M. Auslander …

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 …

We investigate the behavior of the homological dimensions under recollements of derived
categories of algebras. In particular, we establish a series of new bounds among the self …

We give new properties of algebras with finite Gorenstein dimension coinciding with the
dominant dimension $\geq 2$, which are called Auslander-Gorenstein algebras in the …

Over a finite-dimensonal algbera $ A $, simple $ A $-modules that have projective
dimension one have special properties. For example, Geigle-Lenzing studied them in …

Many connections and dualities in representation theory can be explained using quasi-
hereditary covers in the sense of Rouquier. The concepts of relative dominant and …

The main goal of this paper is to compute two related numerical invariants of a primitive
ideal in the universal enveloping algebra of a semisimple Lie algebra. The first one, very …

LetRbe a ring, Pbe a∗-module, andS= EndP. Inspired by the tilting theory, we investigate
relations between the global dimensions gldimRand gldimS, and between the structure of …