Abstract
Denote by𝔄nthe set of alln×nskew-symmetric matrices over the field of real numbers, which forms a Lie ring under the usual matrix addition and the Lie multiplication as[A,B]=AB-BA,A,B∈𝔄n. In this paper, we characterize the automorphism group of the Lie ring𝔄n.
Highlights
Introduction and Main ResultA Lie ring is defined as a nonassociative ring with multiplication that is anticommutative and satisfies the Jacobi identity
It follows from Lemma 6 that there is an orthogonal matrix Q such that φ = Q (ε1 (r) K ⊕ ε2 (r) K) Qt, ∀r ∈ R. (20)
Note that dim C(A) = dim An−2 + 1 = (1/2)(n − 2)(n − 3) + 1 and C(A) has bases which are formed by rank 2 matrices
Summary
Introduction and Main ResultA Lie ring is defined as a nonassociative ring with multiplication that is anticommutative and satisfies the Jacobi identity. Suppose that φ(H) is not a regular matrix, we will get a contradiction. It follows from Lemma 6 that there is an orthogonal matrix Q such that φ (rA) = Q (ε1 (r) K ⊕ ε2 (r) K) Qt, ∀r ∈ R.
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