Density Theorem: Endomorphisms of Simple Modules

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Explores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Covers the properties of finite dimensional algebras and non-semisimple representations.

Covers simple modules, endomorphisms, and Schur's lemma in module theory.

Covers ideals, representations, modules, and maximal ideals in associative algebras.

Covers examples of group algebra decomposition and simple infinite-dimensional algebras.

Covers the structure of finite dimensional algebras and the characterization of semisimple algebras.

Covers the isotopic decomposition of modules into simple components and their properties.

Covers tensor algebras, symmetric and exterior algebras, and tensor products of modules.

Explores Schur's lemma and its applications in representations of an associative algebra over an algebraically closed field.