Enlargements of complexes of fixed size

Fuente: arXiv
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Main Authors: Chaio, Claudia, Chaio, Alfredo Gonzalez, Suarez, Pamela
Format: Preprint
Published: 2025
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author Chaio, Claudia
Chaio, Alfredo Gonzalez
Suarez, Pamela
author_facet Chaio, Claudia
Chaio, Alfredo Gonzalez
Suarez, Pamela
contents Let $A$ be an artin algebra. The aim of this work is to describe the enlargements of an indecomposable complex in $\mathbf{C}_{n}(\mbox{proj} \,A)$, and to study the irreducible morphisms between them. Precisely, we prove that any indecomposable complex in $\mathbf{C}_{[0,n]}(\mbox{proj} \,A)$ or in $\mathbf{C}_{n+1}(\mbox{proj} \,A)$ for $n$ a positive integer is a shift or an enlargement of an indecomposable complex in $\mathbf{C}_{n}(\mbox{proj} \,A)$. We also describe the entrances of the irreducible morphisms in $\mathbf{C}_{[0,n]}(\mbox{proj} \,A)$ between enlargements of an indecomposable complex $X$ in $\mathbf{C}_{n}(\mbox{proj} \,A)$.
format Preprint
id arxiv_https___arxiv_org_abs_2509_12374
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Enlargements of complexes of fixed size
Chaio, Claudia
Chaio, Alfredo Gonzalez
Suarez, Pamela
Representation Theory
16G70, 16G20, 16E10
Let $A$ be an artin algebra. The aim of this work is to describe the enlargements of an indecomposable complex in $\mathbf{C}_{n}(\mbox{proj} \,A)$, and to study the irreducible morphisms between them. Precisely, we prove that any indecomposable complex in $\mathbf{C}_{[0,n]}(\mbox{proj} \,A)$ or in $\mathbf{C}_{n+1}(\mbox{proj} \,A)$ for $n$ a positive integer is a shift or an enlargement of an indecomposable complex in $\mathbf{C}_{n}(\mbox{proj} \,A)$. We also describe the entrances of the irreducible morphisms in $\mathbf{C}_{[0,n]}(\mbox{proj} \,A)$ between enlargements of an indecomposable complex $X$ in $\mathbf{C}_{n}(\mbox{proj} \,A)$.
title Enlargements of complexes of fixed size
topic Representation Theory
16G70, 16G20, 16E10
url https://arxiv.org/abs/2509.12374