The Cartan Matrix of a Centraliser Algebra
Rings and Algebras
2010-12-22 v2
Abstract
The centralizer algebra of a matrix consists of those matrices that commute with it. We investigate the basic representation-theoretic invariants of centralizer algebras, namely their radicals, projective indecomposable modules, injective indecomposable modules, simple modules and Cartan matrices. With the help of our Cartan matrix calculations we determine their global dimensions. Many of these algebras are of infinite global dimension.
Cite
@article{arxiv.math/0611897,
title = {The Cartan Matrix of a Centraliser Algebra},
author = {Umesh V. Dubey and Amritanshu Prasad and Pooja Singla},
journal= {arXiv preprint arXiv:math/0611897},
year = {2010}
}
Comments
8 pages