Standardly stratified lower triangular [formula omitted]-algebras with enough idempotents

Abstract

In this paper we study the lower triangular matrix K-algebra Λ:=[T0MU], where U and T are basic K-algebras with enough idempotents and M is an U-T-bimodule where K acts centrally. Moreover, we characterise in terms of U, T and M when, on one hand, the lower triangular matrix K-algebra Λ is standardly stratified in the sense of [15]; and on the other hand, when Λ is locally bounded in the sense of Gabriel [10]. Finally, we also study several properties relating the projective dimensions in the categories of finitely generated modules mod(U), mod(T) and mod(Λ).