Lectures related to Lie Groups: SU(2) and SO(3)

Symmetries and Groups in Quantum Mechanics

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

Elements of Lie Groups and Algebras

Explores the transformation of vectors and tensors in quantum physics, emphasizing Lie groups and algebras.

Representation Theory: Algebras and Homomorphisms

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

Complete Reducibility of Complex Representations

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

Lie Groups: Representations and Transformations

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

Lie Algebra: Group Theory

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

Group Algebra: Maschke's Theorem

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

General Fields: Lorentz Representations

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

Lie Groups: Structure and Translations

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

Lie Algebras: Introduction and Structure

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

Lie Groups: SU(2) and SO(3)

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

Lie Algebra: Vector Space and Multiplication Law

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

Ideals and Representations

Covers ideals, representations, modules, and maximal ideals in associative algebras.

Exponential Maps: Properties and Applications in Lie Groups

Covers the properties of the exponential map in Lie groups and their algebras, including smoothness and the relationship between subgroups and algebras.

Lie Theorem and Irreducible Representations

Explores the Lie theorem and irreducible representations in group theory.

Linear Transformations: Matrices and Applications

Covers linear transformations using matrices, focusing on linearity, image, and kernel.

Lie Theorems and Group Algebra

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

Group Theory Basics

Introduces the basics of group theory, including operations, properties, and Lie groups.

Lie Group: Structure and Transformations

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

Density Theorem: Endomorphisms of Simple Modules

Covers the density theorem in representation theory, focusing on endomorphisms of simple finite-dimensional modules.