Automorphisms of Chevalley groups of types A l , D l , or E l over local rings with 1/2

Automorphisms of Chevalley groups of different types over commutative rings

“…In the paper [15] of the author it was shown that automorphisms of adjoint elementary Chevalley groups with root systems A l , D l , E l , l 2, over local rings with invertible 2 can be represented as the composition of ring automorphism and an automorphism-conjugation, where as automorphism-conjugation we call a conjugation of elements of a Chevalley group in the adjoint representation by some matrix from the normalizer of this group in GL (V ). In the paper [17] according to the results of [15] it was proved that every automorphism of an arbitrary (elementary) Chevalley group of the described type is standard, i. e., it is represented as the composition of ring, inner, central and graph automorphism. In the same paper it was obtained the theorem describing the normalizer of Chevalley groups in their adjoint representation, which also holds for local rings without 1/2.…”

Normalizers of Chevalley Groups of Type G 2 Over Local Rings Without 1/2

“…An analogue of Proposition 1 and Theorem 2 for root systems A l , D l , and E l was obtained by E. I. Bunina in [4], where all automorphisms of Chevalley groups of given types over local rings with 1/2 were completely described. A similar result for local rings without 1/2 was obtained in [5].…”

The R∞-property for Chevalley groups of types Bl, Nasybullov1 2016Journal of Algebra10080View full textAdd to dashboardCite

“…Using this fact, the proof of the case 3 literally repeats the proof of the case 2 after changing the matrix Z(T ) by the matrix 1 ⊕ Z(T ), and using the result [16] (instead of [14,15]) about the automorphism group of the Chevalley groups of the type B l . Theorem is proved.…”