Abstract
We study the problem of describing local automorphisms of nil-triangular subalgebra of the Chevalley algebra over an associative commutative ring with identity
Highlights
A local automorphism of an algebra A is arbitrary modular automorphism which acts on each element α ∈ A as suitable automorphism of this algebra
According to [1], local automorphisms of the algebra M (n, C) of complex n × n matrices exhausted by automorphisms and anti-automorphisms
In this article we study the more general problem of describing local automorphisms of nil-triangular subalgebra N Φ(K) of the Chevalley algebra over K associated with a root system Φ
Summary
A local automorphism of an algebra A is arbitrary modular automorphism which acts on each element α ∈ A as suitable automorphism of this algebra. R. Crist [3] constructed first example of a nontrivial local automorphism for subalgebra of triangular matrices in M (3, C) with pairwise coincide elements on each diagonal. In [4] and [5] local automorphisms of the algebra N T (n, K) of nil-triangular n × n matrices over K and associated Lie algebra are investigated; they are described for n = 3 and, when K is a field, for n = 4. In this article we study the more general problem of describing local automorphisms of nil-triangular subalgebra N Φ(K) of the Chevalley algebra over K associated with a root system Φ.
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