arXiv subjects

Jakub Kopřiva

Publications and source records attributed to Jakub Kopřiva.

4 recordsLinked to original sources

arXiv2022

Semiorthogonal decompositions for bounded derived categories of gentle algebras

We study semiorthogonal decompositions of bounded derived categories of gentle algebras and how they are manifested in the geometric model of these categories as constructed by Opper, Plamondon and Schroll. We prove that there is a one-to-one correspondence between such semiorthogonal decompositions and suitable cuts of the marked surface underlying the geometric model. Our main tool is the characterization of basis morphisms between indecomposable objects due to Arnesen, Laking and Pauksztello.

math.RT↗

arXiv2021

Ring epimorphisms from path algebras to matrix algebras

In this text, we are concerned with ring epimorphisms, and more specifically universal localisations, from path algebras to matrix algebras. We are mainly focused on constructing ring epimorphisms and universal localisations by extending them from from smaller path algebras to larger path algebras. At first, we discuss some simple results, and then we present generalizations thereof in several directions.

math.RA↗

arXiv2021

Pushouts of affine algebraic sets

We study the problem of existence of pushouts in the category of algebraic sets over an infinite field. This problem can be reduced to asking whether the property of being a finitely generated algebra over a field, or a Noetherian ring in general, is preserved under taking pullbacks. We show that this problem can be fully solved in terms of preservation of this property under taking intersections. In addition, we also discuss specific cases of pushouts of algebraic sets and intersections of Noetherian rings.

math.AC↗

arXiv2017

On the homotopy transfer of $A_\infty$ structures

The present article is devoted to the study of transfers for $A_\infty$ structures, their maps and homotopies, as developed in \cite{Markl06}. In particular, we supply the proofs of claims formulated therein and provide their extension by comparing them with the former approach based on the homological perturbation lemma.

math.AT↗