Lie algebra

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Related lectures (32)

Lie Groups and Lorentz Transformations

Covers Lie groups, Lorentz transformations, boosts, rotations, and complexified Lie algebras.

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.

Complement: Monotone Class Theorem

Explains the independence of events and sets in an algebraic context.

Weyl character formula

Explores the proof of the Weyl character formula for finite-dimensional representations of semisimple Lie algebras.

Lie Theorem and Irreducible Representations

Explores the Lie theorem and irreducible representations in group theory.

The Adjoint Representation

Introduces the concept of the adjoint representation in Lie algebras.

Borcherds' Proof Strategy

Explores Borcherds' proof strategy for monstrous moonshine and Lie superalgebras.

Lie Group: Structure and Transformations

Explores Lie groups, their structure, and applications in transformations.

Simple Lie Algebras: Classification and Properties

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

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.

Properties of Finite Dimensional Algebras

Covers the properties of finite dimensional algebras and non-semisimple representations.

Lie Groups: SU(2) and SO(3)

Covers Lie groups, focusing on SU(2) and SO(3), discussing group structure and representations.

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