Lectures related to Lie Group: Structure and Transformations

General Fields: Lorentz Representations

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

Lie Algebra: Group Theory

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

Nilpotent Lie Groups

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

Jacobi Identity in Lie Algebra

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

Lie Algebra: Vector Space and Multiplication Law

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

Complete Reducibility of Complex Representations

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

Symmetry in Quantum Field Theory

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

Lie Algebra: Casimirs and Poincaré

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

Lie Theorems and Group Algebra

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

Symplectic Geometry

Covers the background on symplectic geometry, focusing on symplectic manifolds and canonical structures.

Simple Lie Algebras: Classification and Properties

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

Macdonald identities

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

Hilpot Liegr: Understanding Nilpotent Lie Groups

Explores nilpotent Lie groups, their orbits, and adjoint actions, illustrating simplicity and form.

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 Groups and Lorentz Transformations

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

Lie Groups: Representations and Transformations

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

Lie Algebra of Lorentz Group

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

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 Groups: SU(2) and SO(3)

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

Elements of Lie Groups and Algebras

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