Lectures related to Lie Theorems and Group Algebra

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

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

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

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

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

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

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

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

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

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

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

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.

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

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

Explores the Kirillov paradigm for the Heisenberg group and unitary representations.

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

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

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

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