Algebras stratified for all linear orders

TL;DR

This paper characterizes finite-dimensional algebras that are stratified for all linear orders, classifies their graded forms as tensor algebras with additional properties, and explores module categories related to these structures.

Contribution

It provides new characterizations of algebras stratified for all linear orders and classifies their graded tensor algebra structures with specific properties.

Findings

Characterizations of algebras stratified for all linear orders

Classification of graded algebras as tensor algebras with extra properties

Analysis of module categories closed under cokernels of monomorphisms

Abstract

In this paper we describe several characterizations of basic finite-dimensional $k$-algebras $A$ stratified for all linear orders, and classify their graded algebras as tensor algebras satisfying some extra property. We also discuss whether for a given preorder $\preccurlyeq$, $\mathcal{F} (_{\preccurlyeq} \Delta)$, the category of $A$-modules with $_{\preccurlyeq} \Delta$-filtrations, is closed under cokernels of monomorphisms, and classify quasi-hereditary algebras satisfying this property.