Let
$${\mathfrak {g}}$$
be a finite-dimensional perfect Lie algebra over a field k of characteristic 0. In infinite-dimensional Lie theory we encounter Lie algebras of the form
$${\mathfrak {g}}\otimes _k R$$
, where R is a k-ring (usually a Laurent polynomial ring in finitely many variables over k), and étale twisted forms
$${\mathcal {L}}$$
of
$${\mathfrak {g}}\otimes _k R$$
. Thus
$${\mathcal {L}}$$
is an R-Lie algebra that becomes isomorphic to the S-Lie algebra
$${\mathfrak {g...
