The Cartan matrix of a centralizer algebra. (English) Zbl 1282.16016
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.
MSC:
| 16G10 | Representations of associative Artinian rings |
| 16S50 | Endomorphism rings; matrix rings |
| 16E10 | Homological dimension in associative algebras |
| 15A30 | Algebraic systems of matrices |
Keywords:
centralizer algebras; Cartan matrices; global dimension; indecomposable modules; simple modulesReferences:
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