Standardly stratified split and lower triangular algebras
Volume 93 / 2002
Colloquium Mathematicum 93 (2002), 303-311
MSC: 16E10, 16G20, 18G20.
DOI: 10.4064/cm93-2-10
Abstract
In the first part, we study algebras $A$ such that $A = R\amalg I$, where $R$ is a subalgebra and $I$ a two-sided nilpotent ideal. Under certain conditions on $I$, we show that $A$ is standardly stratified if and only if $R$ is standardly stratified. Next, for $A=\big[{U\atop M}\, {0\atop V}\big]$, we show that $A$ is standardly stratified if and only if the algebra $R = U \times V$ is standardly stratified and $_VM$ is a good $V $-module.
