Standardly stratified split and lower triangular algebras

Volume 93 / 2002

Eduardo do N. Marcos, Hector A. Merklen, Corina Sáenz 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.

Authors

  • Eduardo do N. MarcosDepartamento de Matemática
    Universidade de São Paulo
    Caixa Postal 66.281
    São Paulo–SP, 05315-970, Brasil
    e-mail
  • Hector A. MerklenDepartamento de Matemática
    Universidade de São Paulo,
    Caixa Postal 66.281
    São Paulo–SP, 05315-970, Brasil
    e-mail
  • Corina SáenzDepartamento de Matemáticas
    Facultad de Ciencias
    Universidad Nacional Autónoma de México
    Circuito Exterior, Ciudad Universitaria
    C.P. 04510, México, D.F., Mexico
    e-mail

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