Structure of Algebras

Related lectures (27)

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

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

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

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

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

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

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

Explains linear independence, bases, and dimension in vector spaces, including the importance of the order of vectors in a basis.