Connected Components

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Related lectures (31)

Page 3 of 4

Group Theory Basics

Introduces the basics of group theory, covering definitions, examples, subgroups, and homomorphisms.

Local Homeomorphisms and Coverings

Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.

Group Theory Basics: Subgroups and Homomorphisms

Introduces subgroups and homomorphisms in group theory, with examples for illustration.

Further Directions: Algebraic Groups

Explores various directions for studying algebraic groups and offers references for further exploration.

Modules of Covariants

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

Linear Representations: Basics and Examples

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

Group Actions: Differential of Orbit Map

Explores the differential of group actions on vector spaces and the behavior of orbit maps.

The Regular Representation

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

Connected groups of semisimple elements

Explores weight space decomposition and proves that a connected linear algebraic group with all semi-simple elements must be a torus.

Endomorphisms and automorphisms of totally disconnected locally compact groups I

Covers the definitions and basic results of endomorphisms and automorphisms of totally disconnected locally compact groups.