Linearly reductive groupsDiscusses linearly reductive groups and their properties, focusing on completely reducible representations and equivalent modules.
Quotient CriterionExplores a criterion for computing quotients in algebraic geometry, emphasizing the importance of normality and g-invariant morphisms.
Remarks about the QuotientExplores the concept of the quotient in linearly reductive groups and varieties, discussing irreducibility, normality, and integral properties.
Connected ComponentsCovers the concept of connected components in linear algebraic groups and their relationship to singular groups.
Diagonalizable GroupsExplores the concept of diagonalizable groups and their properties in linear algebraic groups.
Fundamental GroupsExplores fundamental groups, homotopy classes, and coverings in connected manifolds.
Modules of CovariantsExplores the decomposition of the circle of the coordinate ring of a G variety into a direct sum of simple submodules.
Subgroups and subalgebrasExplores the unique determination of homomorphisms by differentials and the intersection of closed subgroups' Lie algebras.
Topological GroupsCovers the definition and examples of topological groups, focusing on actions of groups on spaces.
