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

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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.