A proof of the finite generation of invariants of a normal subgroup

John Brendan Sullivan

Vol. 51 (1974), No. 2, 571–572

DOI: 10.2140/pjm.1974.51.571

Abstract

A fundamental theorem in the development of the quotient theory of an affine algebraic group G shows that the coordinate functions invariant under a normal subgroup form a finitely generated algebra. We show that this theorem follows from the finite field generation of the quotient field of the algebra of invariant coordinate functions in the connected case.

Mathematical Subject Classification

Primary: 20F30

Milestones

Received: 2 February 1973

Published: 1 April 1974