Journal of Siberian Federal University. Mathematics & Physics / On Centralizers of the Graph Automorphisms of Niltriangular Subalgebras of Chevalley Algebras

Full text (.pdf)
Issue
Journal of Siberian Federal University. Mathematics & Physics. 2022 15 (5)
Authors
Levchuk, Vladimir M.; Suleimanova, Galina S.
Contact information
Levchuk, Vladimir M.: Siberian Federal University Krasnoyarsk, Russian Federation; ; Suleimanova, Galina S.: Siberian Federal University Krasnoyarsk, Russian Federation;
Keywords
Chevalley algebra; niltriangular subalgebra; homomorphisms of root systems
Abstract

Graph automorphisms of a Chevalley group correspond to each type of reduced indecompos- able root system , which Coxeter graph has a non-trivial symmetry. It is well-known, that a Chevalley algebra and its niltriangular subalgebra N has a graph automorphism exaclty when is of type An, Dn or E6. We note connections with homomorphisms of root systems introduced in 1982. The main theorem on the centralizers in N of the automorphism gives new representations of niltriangular subalgebras, using also the unique series of unreduced indecomposable root system of type BCn.

Pages
679–682
DOI
10.17516/1997-1397-2022-15-5-679-682
Paper at repository of SibFU
https://elib.sfu-kras.ru/handle/2311/149162