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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| Veröffentlicht in: | Proceedings of the Indian Academy of Sciences. Mathematical sciences 2012-02, Vol.122 (1), p.67-73 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
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| Online-Zugang: | Volltext |
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| Zusammenfassung: | 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. |
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| ISSN: | 0253-4142 0973-7685 |
| DOI: | 10.1007/s12044-012-0059-6 |