The Cartan Matrix of a Centraliser Algebra

Details The Cartan Matrix of a Centraliser Algebra The Cartan Matrix of a Centraliser Algebra

2006-11-29

arxiv.org/abs/math/0611897v2

Mathematics

Rings and Algebras

8 pages

Scientific paper

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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