2 citations · 6 across the 8 of their papers we have counts for
11 papers
Relative Global Dimension of Controllable Extensions
Kostiantyn Iusenko, Roger R. Primolan
We study relative global dimensions of extensions of Artin algebras over a perfect field. A controllable extension is introduced as one for which the relative globa…
Stability for socle-projective categories of type
Kostiantyn Iusenko, Gabriel Bravo Rios, Robinson-Julian Serna
We extend the notion of stability in the non-abelian category of poset representations (introduced by Futorny and Iusenko) to the category of socle-projective representations of a…
A relative homology criterion of smoothness
Kostiantyn Iusenko, Eduardo do Nascimento Marcos, Victor do Valle Pretti
We investigate the relationship between smoothness and the relative global dimension of a ring extension. We prove that a smooth commutative algebra over has finite relativ…
Semisimplicity and separability for pseudocompact algebras
Kostiantyn Iusenko, John MacQuarrie
In this expository article, we give a self-contained introduction to the wonderfully well-behaved class of pseudocompact algebras, focusing on the foundational classes of semisimpl…
Homological properties of extensions of algebras
Kostiantyn Iusenko, John W. MacQuarrie
We consider a class of extensions of associative algebras, which we refer to as ``strongly proj-bounded extensions''. We prove that the finiteness of the left global dimension and…
A functorial approach to Gabriel -quiver constructions for coalgebras and pseudocompact algebras
Kostiantyn Iusenko, John William MacQuarrie, Samuel Quirino
We define the path coalgebra and Gabriel quiver constructions as functors between the category of -quivers and the category of pointed -coalgebras, for a field. We define…
On dimension of poset variety
Claudia Cavalcante Fonseca, Kostiantyn Iusenko
For a finite partially ordered set we calculate the dimension of the variety of its subspace representations having fixed dimension vector. The dimension is given in terms of the E…
Stable representations of posets
Vyacheslav Futorny, Kostiantyn Iusenko
The purpose of this paper is to study stable representations of partially ordered sets (posets) and compare it to the well known theory for quivers. In particular, we prove that ev…
Quivers, Algebras and Adjoint functors
Kostiantyn Iusenko
These are the notes for a minicourse held in Odessa (2016) and Belo Horizonte (2017). My aim was to provide a short introduction to basic notions of category theory and representat…
The path algebra as a left adjoint functor
Kostiantyn Iusenko, John MacQuarrie
We consider an intermediate category between the category of finite quivers and a certain category of pseudocompact associative algebras whose objects include all pointed finite di…
Some remarks on Hall algebra of bound quiver
Kostiantyn Iusenko, Evan Wilson
In this paper we describe the twisted Hall algebra of bound quiver with small homological dimension. The description is given in the terms of the quadratic form associated with the…