Cycle-finite module categories
Piotr Malicki, Jos\'e A. de la Pe\~na, Andrzej Skowro\'nski
TL;DR
This paper characterizes finite-dimensional algebra module categories where cycles of nonisomorphic indecomposable modules are finite, and explores their geometric and homological properties.
Contribution
It provides a detailed description of cycle-finite module categories and investigates their geometric and homological aspects.
Findings
Cycle-finite module categories have a well-defined structure.
The paper reveals specific geometric properties of these categories.
Homological characteristics of cycle-finite categories are analyzed.
Abstract
We describe the structure of module categories of finite dimensional algebras over an algebraically closed field for which the cycles of nonzero nonisomorphisms between indecomposable finite dimensional modules are finite (do not belong to the infinite Jacobson radical of the module category). Moreover, geometric and homological properties of these module categories are exhibited.
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