Concept

Lie algebra

Related lectures (32)

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

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

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

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

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

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

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

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

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

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

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

Explores nilpotent Lie groups, their orbits, and adjoint actions, illustrating simplicity and form.

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

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

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

Covers the background on symplectic geometry, focusing on symplectic manifolds and canonical structures.

Covers the role of symmetries and groups in quantum mechanics, focusing on SU2 and SU3, their properties, and implications for physical theories.

Covers dynamical systems on homogeneous spaces and their interactions with number theory.

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

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