Lectures related to Diagonalizable Groups

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

Explores chirality, group completeness, Abelian groups, conjugate classes, and isomorphic groups in symmetry and group theory.

Explores automorphism groups of trees and graphs, including actions on trees and group homomorphisms.

Explores the Hopf formula in cohomology groups, emphasizing the 4-term exact sequence and its implications.

Covers the properties of commutative linear algebraic groups and their elements.

Explores the unique determination of homomorphisms by differentials and the intersection of closed subgroups' Lie algebras.

Covers the concept of connected components in linear algebraic groups and their relationship to singular groups.

Covers linear representations, isomorphism, G modules, and classification of representations of C star and C plus.

Explores constructing quotients of linear algebraic groups by linearly reductive sub-groups.

Covers linear algebraic groups, including special sets and matrix examples.

Delves into the Jordan decomposition in Lie algebras of linear algebraic groups.

Explores weight space decomposition and proves that a connected linear algebraic group with all semi-simple elements must be a torus.

Discusses linear Lie groups, their definitions, properties, and the relationship between integral curves and vector fields.

Explores the universal property of groups, defining homomorphisms and exploring subgroup properties.

Covers the isotopic decomposition of modules into simple components and their properties.

Explores symplectic groups, linear transformations preserving non-degenerate alternating bilinear forms on vector spaces.

Explores the embedding of chi-varieties into vector spaces with linear actions.

Explores Schur's lemma and its applications in representations of an associative algebra over an algebraically closed field.

Explores various directions for studying algebraic groups and offers references for further exploration.