On the group of Lie-orthogonal operators on a Lie algebra - Petravchuk, A. P.; Maksimenko, D. V.; Bilun, S. V. (Methods of Functional Analysis and Topology, 2011)
Finite dimensional Lie algebras over the field of complex numbers with a linear operator T: L→ L such that [T(x),T(y)]=[x,y] for all x,yL are studied. The group of such non-degenerative linear operators on L is considered. Some properties of this group and its relations with the group Aut(L) in the general linear group GL(L) are described.