Recap of Group TheoryProvides a recap of group theory, defining a group as a set with a multiplication operation.
Subgroups and subalgebrasExplores the unique determination of homomorphisms by differentials and the intersection of closed subgroups' Lie algebras.
Linearly reductive groupsDiscusses linearly reductive groups and their properties, focusing on completely reducible representations and equivalent modules.
Concrete CategoriesCovers concrete categories with sets and structures, including Ens, Gr, Ab, and Vectk.
Fundamental GroupsExplores fundamental groups, homotopy classes, and coverings in connected manifolds.
Isotypic DecompositionCovers the isotopic decomposition of modules into simple components and their properties.
Diagonalizable GroupsExplores the concept of diagonalizable groups and their properties in linear algebraic groups.
Connected ComponentsCovers the concept of connected components in linear algebraic groups and their relationship to singular groups.
Group HomomorphismsExplores group homomorphisms, isomorphisms, and generators in abstract algebra.
Group Theory BasicsIntroduces the basics of group theory, covering definitions, examples, subgroups, and homomorphisms.
Group CohomologyCovers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.
