Lectures related to Affine Lie algebra

Macdonald identities

Delves into Macdonald identities, covering affine root systems, modular forms, and Lie algebras.

Lie Algebra: Casimirs and Poincaré

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

Lie Algebra: Group Theory

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

Symmetry in Quantum Field Theory

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

Simple Lie Algebras: Classification and Properties

Explores the classification and properties of simple complex Lie algebras, emphasizing their connection with Lie groups.

Lie Theorems and Group Algebra

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

Complete Reducibility of Complex Representations

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

Quantum Field Theory: Poincaré Group

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

Lie Algebra: Representations

Explores Lie algebra representations, emphasizing SU(2) and traceless matrices, explained by Alfredo Glioti.

Lie Algebra: Vector Space and Multiplication Law

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

Lie Algebra: Basics and Applications

Covers the basics of Lie algebra and its applications in linear equations and Einstein tensor calculations.

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.

Lie Algebra of Lorentz Group

Covers the Lie algebra of the Lorentz group, focusing on boosts, rotations, and transformations.

Kirillov Paradigm for Heisenberg Group

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

McKay Correspondence and Coxeter Groups

Explores the McKay correspondence, Coxeter groups, and finite subgroups of SU(2) and SO(3, emphasizing odd order properties and root system constructions.

Jacobi Identity in Lie Algebra

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

Easing Model Conformal Theory: Scaling Limits and Correlations

Covers the Easing model conformal theory, focusing on scaling limits and correlation functions.

Vector Fields

Explains vector fields as derivations and their algebraic structure in Lie algebra.

Central Results in Hermite Forms

Covers central results in Hermite forms and principal series representations in group theory.

Quantum Field Theory: Exo Session 4

Covers exercises on Schur's lemma and the Jacobi identity in Quantum Field Theory.