
TL;DR
This paper provides a combinatorial criterion to identify Laura algebras among special biserial algebras and proves a conjecture relating finiteness of certain indecomposable modules to the Laura property.
Contribution
It introduces a simple criterion for recognizing Laura algebras and proves a conjecture linking the Laura property to finiteness of specific indecomposable modules.
Findings
A combinatorial criterion for Laura algebras is established.
A special biserial algebra is Laura iff it has finitely many indecomposables with certain dimension properties.
The conjecture by Skowronski is confirmed for special biserial algebras.
Abstract
We give a simple combinatorial criterion allowing to recognize whether a string (or, more generally, a special biserial) algebra is a laura algebra or not. We also show that a special biserial algebra is laura if and only if it has a finite number of isomorphism classes of indecomposable modules which have projective dimension and injective dimension greater than or equal to two, solving a conjecture ok Skowronski for special biserial algebras.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Rings, Modules, and Algebras · Coding theory and cryptography
