Concept

Lie algebra representation

Related lectures (32)

Explores Lie Algebra's connection to Group Theory through associative operations and Jacobi identities.

Explores Lie algebra, Casimirs, and Poincaré in SO(3) transformations.

Explores Lie algebras, representations, tensor products, and commutation relations in mathematics.

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

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

Explores associativity, Lie algebra, Lie groups, relativity, and symmetry preservation in quantum field theory.

Explores the Kirillov paradigm for the Heisenberg group and unitary representations.

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

Covers the complete reducibility of complex representations and the relation between Lie algebras and Lie groups.

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

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

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

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

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.

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

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

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

Explores symmetry operations, isomorphic representations, and three-dimensional group representations.

Explores Einsteinian relativity, the Lorentz group, and Poincaré transformations, emphasizing proper and non-orthochronous components.