Lectures related to Group Theory - Part 2

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

Groups: Definitions, Properties, and Homomorphisms

Introduces the basic concepts of groups, including definitions, properties, and homomorphisms, with a focus on subgroup properties and normal subgroups.

Abelian Groups: Free Abelian Groups

Explores free abelian groups, homomorphisms, and exact sequences in group theory.

Categorical Perspective: Abelian Groups

Explores abelian groups from a categorical perspective, discussing the coproduct construction.

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Exact Sequences: Torsion and Divisibility

Explores exact sequences of abelian group homomorphisms and provides examples.

Hom Functor: Abelian Groups

Explores the Hom functor for abelian groups and its relation to direct sums.

Representation Theory: Algebras and Homomorphisms

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

Group Direct Sums in Group Theory

Explores direct sums in group theory, focusing on abelian groups and their implications.

Group Cohomology

Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.