Geodesic
On centralizers of the graph automorphisms of niltriangular subalgebras of Chevalley algebras
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 5, pp. 679-682

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Graph automorphisms of a Chevalley group correspond to each type of reduced indecomposable root system $\Phi$, 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 $\theta$ exaclty when $\Phi$ is of type $A_n$, $D_n$ or $E_6$. We note connections with homomorphisms of root systems introduced in 1982. The main theorem on the centralizers in $N$ of the automorphism $\theta$ gives new representations of niltriangular subalgebras, using also the unique series of unreduced indecomposable root system of type $BC_n$.
Keywords: Chevalley algebra, homomorphisms of root systems.
Mots-clés : niltriangular subalgebra 
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     title = {On centralizers of the graph automorphisms of niltriangular subalgebras of {Chevalley} algebras},
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Vladimir M. Levchuk; Galina S. Suleimanova. On centralizers of the graph automorphisms of niltriangular subalgebras of Chevalley algebras. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 5, pp. 679-682. http://geodesic.mathdoc.fr/item/JSFU_2022_15_5_a15/