Subgroups and subalgebras

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Related lectures (32)

Linear Representations: Basics and Examples

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

Local structure of totally disconnected locally compact groups I

Covers the local structure of totally disconnected locally compact groups, exploring properties and applications.

Lie Theorems and Group Algebra

Covers Lie theorems, group algebra, Ado's theorem, and spacetime symmetries.

Linearly reductive groups

Discusses linearly reductive groups and their properties, focusing on completely reducible representations and equivalent modules.

Automorphism Groups: Trees and Graphs III

Explores automorphism groups of trees and graphs, including actions on trees and group homomorphisms.

Group Actions: Differential of Orbit Map

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

Lie Algebra: Representations and Symmetry Groups

Covers Lie algebra, group representations, symmetry groups, and Schur's lemma in the context of symmetry and group operations.

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McKay Correspondence and Coxeter Groups

Explores the McKay correspondence, Coxeter groups, and finite subgroups of SU(2) and SO(3, emphasizing odd order properties and root system constructions.

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.

Nilpotent Lie Groups

Covers the properties of nilpotent Lie groups and the construction of non-degenerate alternating 2-forms.

General Fields: Lorentz Representations

Covers the representation of Lorentz transformations through general fields and the consequences of symmetry.

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