Automorphism group schemes and Weyl groups of gradings
Abstract
A scheme theoretic version of the automorphism group of a grading on an algebra is presented, and the classical result that shows that, over algebraically closed fields of characteristic [Formula: see text], the automorphism group of a grading is the normalizer of its diagonal group is extended, over arbitrary fields, to this scheme setting. The quotient of the scheme theoretic versions of the automorphism group and the stabilizer of a grading turns out to be a constant group scheme, called the Weyl group scheme of the grading. For algebraically closed fields this is the constant group scheme associated to the ordinary Weyl group of the grading, but this fails over arbitrary fields.
Fields of Study & Subjects
Advanced Algebra and Geometry
Advanced Topics in Algebra
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- International Journal of Algebra and Computation
- Publisher
- World Scientific Pub Co Pte Ltd
- Pages
- 1–12
- Publication date
- 14 May 2026
- Language
- EN