Lie Algebra: Basics and Applications

Related lectures (38)

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

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

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

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

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

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

Covers Lie Algebra, focusing on vector space and multiplication law.

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.

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

Covers the Lie algebra of the Lorentz group, focusing on boosts, rotations, and transformations.

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

Covers exercises on Schur's lemma and the Jacobi identity in Quantum Field Theory.

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

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

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

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

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

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

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

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