Lie Theorems and Group Algebra

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Related lectures (31)

Lie Algebra Representation

Delves into Lie algebra representation and Lorentz subgroup concepts.

Exponential Maps: Properties and Applications in Lie Groups

Covers the properties of the exponential map in Lie groups and their algebras, including smoothness and the relationship between subgroups and algebras.

QED: Gauge Theories

Covers Quantum Electrodynamics (QED), instantons, Feynman rules, and gauge theories in modern particle physics.

Simple Lie Algebras: Classification and Properties

Explores the classification and properties of simple complex Lie algebras, emphasizing their connection with Lie groups.

Macdonald identities

Delves into Macdonald identities, covering affine root systems, modular forms, and Lie algebras.

Group Actions: Differential of Orbit Map

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

Weil Representation and Heis Operators

Covers the Weil representation, Heis operators, Stone-Neumann theorem, unitary operators, Lie algebra structure, and symplectic form.

Ideals and Representations

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

Structure of Algebras

Covers the structure of finite dimensional algebras and the characterization of semisimple algebras.

Lie Algebra: Representations

Explores Lie algebra representations, emphasizing SU(2) and traceless matrices, explained by Alfredo Glioti.

Lie Theorem and Irreducible Representations

Explores the Lie theorem and irreducible representations in group theory.

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