Lectures related to Lie Groups: Structure and Translations

Explores Cayley tables, group operations, homomorphisms, Lie groups, and differentiable groups.

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

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 Lie theorem and irreducible representations in group theory.

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

Explores Schur's lemma and its applications in representations of an associative algebra over an algebraically closed field.

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

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

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

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

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

Covers the theory of time inversion operator and Lie groups, discussing the consequences of the Wigner theorem.

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

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

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

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

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