Linear Representations: Basics and Examples

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Related lectures (27)

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Concrete Categories

Covers concrete categories with sets and structures, including Ens, Gr, Ab, and Vectk.

Cohomology: Cross Product

Explores cohomology and the cross product, demonstrating its application in group actions like conjugation.

Decomposition of Group Algebras

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

G-modules and G-varieties

Explores the embedding of chi-varieties into vector spaces with linear actions.

Universal Property of Groups

Explores the universal property of groups, defining homomorphisms and exploring subgroup properties.

Linear Applications: Definitions and Properties

Explores the definition and properties of linear applications, focusing on injectivity, surjectivity, kernel, and image, with a specific emphasis on matrices.

Categorical Perspective: Group Actions

Generalizes group actions beyond sets, providing a comprehensive framework for various mathematical contexts.

Module Theory: Chain Conditions

Explores chain conditions in module theory, emphasizing Noetherian modules and stabilizing sequences of submodules.

Subrepresentations of the regular representation

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

Pushouts in Group Theory: Universal Properties Explained

Covers the construction and universal properties of pushouts in group theory.