Lectures related to Group Theory Basics

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

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

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

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

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

Explores symmetries in physics through group theory, emphasizing how symmetries keep equations of motion unchanged.

Covers the construction and universal properties of pushouts in group theory.

Covers the basics of group theory, including definitions, examples, and isometries.

Covers cohomology in real projective spaces, focusing on associative properties and algebraic structures.

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

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

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

Presents the classification of finite abelian groups as products of cyclic groups, a fundamental result in various branches of mathematics.

Delves into group theory, emphasizing the centralizer of elements and the classification of finite abelian groups.

Introduces group theory concepts, including definitions and properties of groups, rings, and fields.

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

Explores the construction of the Fischer-Greiss monster group, emphasizing its key properties and the process involved.

Explores the group structure and isomorphism of elliptic curves, including inverses, associativity, and compactification to the torus.

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