Lectures related to Lie Theorem and Irreducible Representations

Representation Theory: Algebras and Homomorphisms

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

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

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

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

Lie Groups: Representations and Transformations

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

Complete Reducibility of Complex Representations

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

Lie Algebra: Group Theory

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

Group Theory & Quantum Mechanics

Explores k-fold degenerate sets of eigenfunctions and their basis for irreducible representations.

General Fields: Lorentz Representations

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

Tensor Products of Modules

Covers tensor algebras, symmetric and exterior algebras, and tensor products of modules.

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.

Symmetry and Group Theory: Exercise 5

Covers the basis for irreducible representations and characters of direct product representations.

Lie Theorems and Group Algebra

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

Lie Groups and Lorentz Transformations

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

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

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

Group representations constructions

Explores the construction of group representations through various methods and provides an illustrative example using the standard representation of sr2 on c2.

Lie Algebra: Representations and Symmetry Groups

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

Representations of SU(2): Symmetries and Transformations

Covers the representations of SU(2) and their transformations in quantum mechanics.

Decomposition of Group Algebras

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

Jacobi Identity in Lie Algebra

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