Explores the concept of diagonalizable groups and their properties in linear algebraic groups.
Covers the concept of connected components in linear algebraic groups and their relationship to singular groups.
Explores fundamental groups, homotopy classes, and coverings in connected manifolds.
Explores the unique determination of homomorphisms by differentials and the intersection of closed subgroups' Lie algebras.
Explores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.
Explores the decomposition of the circle of the coordinate ring of a G variety into a direct sum of simple submodules.
Explores the Mayer-Vietoris sequence, exact homomorphisms, embedded spheres, and path-connected spaces.
Explores chirality, group completeness, Abelian groups, conjugate classes, and isomorphic groups in symmetry and group theory.
Covers quotients in abelian groups and the concept of free abelian groups, showing that every abelian group is isomorphic to a quotient of a free abelian group.
Covers concrete categories with sets and structures, including Ens, Gr, Ab, and Vectk.
