The Automorphism Group of the Lie Ring of Real Skew-Symmetric Matrices

Abstract

Denote by ${𝔄}_n$ the set of all $n\times n$ skew-symmetric matrices over the field of real numbers, which forms a Lie ring under the usual matrix addition and the Lie multiplication as $[A,B]=AB-BA$, $A,B\in {𝔄}_n$. In this paper, we characterize the automorphism group of the Lie ring ${𝔄}_n$.