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Concept

Lie group–Lie algebra correspondence

Related lectures (31)

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

Explores associativity, Lie algebra, Lie groups, relativity, and symmetry preservation in quantum field theory.

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

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

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

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

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

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.

Covers Lie algebra, group representations, symmetry groups, and Schur's lemma in the context of symmetry and group operations.

Explores the Lie theorem and irreducible representations in group theory.

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

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

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

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

Covers Lie groups, Lorentz transformations, boosts, rotations, and complexified Lie algebras.

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

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

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

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