Lie Algebras and Representations

Related lectures (42)

Explores the transformation of vectors and tensors in quantum physics, emphasizing Lie groups and algebras.

Explores Lie groups, scalar fields, and vector spaces transformations.

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

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

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

Covers singular vectors in Liouville CFT, focusing on representation theory and their implications in mathematical physics.

Explores the Lie theorem and irreducible representations in group theory.

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

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

Explores the significance of the Jacobi identity in Lie algebra and its impact on linear vector spaces.

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

Explains the tensor product of representations in quantum physics and the properties of defined actions.

Covers the basics of group theory, including sets, applications, and examples like permutations and rotations.

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

Covers the representation theory of unitary minimal models and the Virasoro algebra.

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Covers tensor algebras, symmetric and exterior algebras, and tensor products of modules.

Explores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.

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

Explores Schur's lemma and its applications in representations of an associative algebra over an algebraically closed field.

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