Lectures related to Structure of Algebras

Explores identical applications in linear algebra, discussing their representation and implications through examples and equation solving.

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

Explores orthogonality between vectors and subspaces, demonstrating practical implications in matrix operations.

Explains linear independence, basis, and matrix rank with examples and exercises.

Explores the proof of the Weyl character formula for finite-dimensional representations of semisimple Lie algebras.

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

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