Lectures related to Lie Algebra: Representations

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

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

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

Covers the basics of group theory, including sets, applications, and examples like permutations and rotations.

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

Explores the transformation of vectors and tensors, including rotations and representations in quantum physics.

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

Covers the Lie algebra of the Lorentz group, focusing on boosts, rotations, and transformations.

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

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

Covers angular momentum in rotations, including preservation of angles and vector products.

Covers Quantum Electrodynamics (QED), instantons, Feynman rules, and gauge theories in modern particle physics.

Explores Lie groups, scalar fields, and vector spaces transformations.

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

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

Explores Lie algebras, representations, tensor products, and commutation relations in mathematics.

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Explores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.

Covers examples of group algebra decomposition and simple infinite-dimensional algebras.

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