Lie Algebra: Vector Space and Multiplication Law

Related lectures (30)

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

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

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

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

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

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

Explores the differential of group actions on vector spaces and the behavior of orbit maps.

Explores quadratic forms, symmetric bilinear forms, and their properties.

Explores polynomial operations, properties, and subspaces in vector spaces.

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