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.
Fundamental GroupsExplores fundamental groups, homotopy classes, and coverings in connected manifolds.
Subgroups and subalgebrasExplores the unique determination of homomorphisms by differentials and the intersection of closed subgroups' Lie algebras.
Group Algebra: Maschke's TheoremExplores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.
