Representation Theory: Algebras and Homomorphisms

Related lectures (26)

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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.

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

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

Covers the density theorem in representation theory, focusing on endomorphisms of simple finite-dimensional modules.

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

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

Explores Lie groups, scalar fields, and vector spaces transformations.

Explores Lie algebras, representations, tensor products, and commutation relations in mathematics.

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

Explores Lie Algebra's connection to Group Theory through associative operations and Jacobi identities.