Lie Group: Structure and Transformations

Related lectures (32)

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

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

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

Introduces the concept of the adjoint representation in Lie algebras.

Explores the properties of the exponential map in Lie groups and algebras.

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

Explores the unique determination of homomorphisms by differentials and the intersection of closed subgroups' Lie algebras.

Explores Lie groups SU(2) and SO(3), emphasizing their mathematical properties and significance in physics.

Discusses linear Lie groups, their definitions, properties, and the relationship between integral curves and vector fields.

Introduces Lie algebras, vector spaces with a special bracket operation.

Explores Borcherds' proof strategy for monstrous moonshine and Lie superalgebras.

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

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