Representations of Finite-dimensional Algebras
In modular representation theory, and more generally in the theory of representations of finite-dimensional associative algebras A that are not semisimple, a Cartan matrix is defined by considering a (finite) set of principal indecomposable modules and writing composition series for them in terms of irreducible modules, yielding a matrix of integers counting the number of occurrences of an irreducible module.
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