The Cartan matrix of a centralizer algebra

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. W...

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Bibliographic Details
Published inProceedings of the Indian Academy of Sciences. Mathematical sciences Vol. 122; no. 1; pp. 67 - 73
Main Authors DUBEY, UMESH V, PRASAD, AMRITANSHU, SINGLA, POOJA
Format Journal Article
LanguageEnglish
Published India Springer-Verlag 01.02.2012
Subjects
Mathematics
Mathematics and Statistics
global dimension
Cartan matrix
Centralizer algebras
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Summary: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.
ISSN:0253-4142
0973-7685
DOI:10.1007/s12044-012-0059-6