Automorphisms of quotients of ΠGL(n_i)

William Charles Waterhouse

Vol. 102 (1982), No. 1, 221–233

DOI: 10.2140/pjm.1982.102.221

Abstract

Quotients of GL(n) by finite subgroups can have radial algebraic automorphisms. More generally, quotients of Π₁^sGL(n_i) by (s − 1)-dimensional central subgroups can have automorphisms not induced by automorphisms of ΠGL(n_i). This paper works out an explicit description of all their algebraic group automorphisms. As a sample application, the normalizer of the GL(n)-action on Λ^r(kⁿ) is computed.

Mathematical Subject Classification 2000

Primary: 20G15

Secondary: 14L40

Milestones

Received: 12 August 1981

Revised: 24 November 1981

Published: 1 September 1982