Subgroups and subalgebrasExplores the unique determination of homomorphisms by differentials and the intersection of closed subgroups' Lie algebras.
Fundamental GroupsExplores fundamental groups, homotopy classes, and coverings in connected manifolds.
Connected ComponentsCovers the concept of connected components in linear algebraic groups and their relationship to singular groups.
Isotypic DecompositionCovers the isotopic decomposition of modules into simple components and their properties.
Symplectic GroupsExplores symplectic groups, linear transformations preserving non-degenerate alternating bilinear forms on vector spaces.
Symmetry and Group TheoryExplores chirality, group completeness, Abelian groups, conjugate classes, and isomorphic groups in symmetry and group theory.
