On Centralizers of the Graph Automorphisms of Niltriangular Subalgebras of Chevalley Algebras

Graph automorphisms of a Chevalley group correspond to each type of reduced indecompos-able root system di, 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 d 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 0 gives new representations of niltriangular subalgebras, using also the unique series of unreduced indecomposable root system of type BCn.