Trisections of module categories
Volume 107 / 2007
Colloquium Mathematicum 107 (2007), 191-219
MSC: 16G60, 16G20, 16G70, 18G20.
DOI: 10.4064/cm107-2-3
Abstract
Let $A$ be a finite-dimensional algebra over a field $k$. We discuss the existence of trisections $(\mathop{\rm mod}\nolimits_+A,\mathop{\rm mod}\nolimits_0A,\mathop{\rm mod}\nolimits_-A)$ of the category of finitely generated modules $\mod A$ satisfying exactness, standardness, separation and adjustment conditions. Many important classes of algebras admit trisections. We describe a construction of algebras admitting a trisection of their module categories and, in special cases, we describe the structure of the components of the Auslander–Reiten quiver lying in $\mathop{\rm mod}\nolimits_0A$.
