Concept

Lie group

Related lectures (30)

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

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

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

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

Explores the Lie theorem and irreducible representations in group theory.

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

Explores Lie groups, translations, and invariance of states under transformations.

Explores Cayley tables, group operations, homomorphisms, Lie groups, and differentiable groups.

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

Introduces the basics of group theory, including operations, properties, and Lie groups.

Explores gauge symmetries in quantum field theory, emphasizing invariance under transformations and the role of ghost fields.

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

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

Explores the consequences of symmetry, focusing on the Noether Theorem and coordinated charges in Lie groups.

Covers the electromagnetic field in astrophysics and field theory, including the symmetry principle and interaction terms.

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

Explores integral curves on manifolds and the significance of the exponential map in Lie groups.

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

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

Explores the dynamical consequences of symmetry, emphasizing conservation laws and the role of Noether currents.