G-modules and G-varieties

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Related lectures (31)

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The Regular Representation

Introduces the regular representation, a key tool for studying group actions on varieties.

Group Algebra: Maschke's Theorem

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

Subrepresentations of the regular representation

Explores subrepresentations of the regular representation in group theory, emphasizing properties and isomorphism between subrepresentations.

Linear Representations: Basics and Examples

Covers linear representations, isomorphism, G modules, and classification of representations of C star and C plus.

Modules of Covariants

Explores the decomposition of the circle of the coordinate ring of a G variety into a direct sum of simple submodules.

Ideals and Representations

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

Isotypic Decomposition

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

Decomposition of Group Algebras

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

Group representations constructions

Explores the construction of group representations through various methods and provides an illustrative example using the standard representation of sr2 on c2.

Representation Theory: Algebras and Homomorphisms

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