Groups of Automorphisms of Chevalley Algebras

Automorphisms Group of an Invariant Subalgebra of a Reductive Lie Algebra

“…In the proof of Theorem 1, we apply numerous properties of centroid from these articles. In the recent paper [6] we have proved Theorem 1, similar to Corollary 2 for nilpotent invariant subalgebras of Chevalley algebras only but over the field K of arbitrary characteristic. It seems interesting to extend the statement of Theorem 1 to modular Lie algebras.…”

“…The proof of Theorem 1 is based on the statement about rigid algebras. PROPOSITION 5 (Proposition 4 [6]). Let K/L be any extension of fields and V be a finite-dimensional rigid (nonassociative) algebra over L. Then if L is a maximal field of scalars for V , tensor completion U = V ⊗ L K has a standard group of automorphisms Aut L (U ) = Aut L K (Aut K (U ) · SpAut L (U )).…”

“…Under the conditions of Corollary 2, the algebra U is generated by some part of the Chevalley basis for R (see [1,6]). The structure constants of the Chevalley basis are integer numbers.…”