Quotients of Linear Groups by Linearly Reductive Groups

This lecture explains how to construct quotients of linear algebraic groups by linearly reductive sub-groups, showing that the resulting quotients are geometric and have a group structure induced from the original group. The instructor demonstrates that the multiplication and inversion operations on the quotient group are regular morphisms, providing a detailed proof based on the universal property of the quotient map. The lecture concludes by highlighting the existence of quotients by arbitrary closed normal subgroups, leading to the formation of a new linear algebraic group.