Lectures related to Lie Algebra: Group Theory

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

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

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

Covers simplicial and cosimplicial objects in category theory with practical examples.

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

Covers the basics of group theory, including elements, associativity, identity, inverses, and closure.

Covers the basics of group theory, including sets, applications, and examples like permutations and rotations.

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

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

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.

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

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

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

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

Explores the local structure of totally disconnected locally compact groups and their isomorphisms through conjugation.

Explores the composition of applications in mathematics and the importance of understanding their properties.

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

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

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