Lie Algebra: Basics and Applications

Related lectures (32)

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

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

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 the Kirillov paradigm for the Heisenberg group and unitary representations.

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

Explores the classification and properties of simple complex Lie algebras, emphasizing their connection with Lie groups.

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.

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