“…Just as the tangent algebra of a Lie group is a Lie algebra, the tangent algebra of a locally analytic Moufang loop is a Malcev algebra [26-28, 46, 53, 58], see also [17,52,54] for discussions about connections with physics. The notion of pre-Malcev algebra as a Malcev algebraic analogue of a pre-Lie algebra was introduced in [41]. A pre-Malcev algebra is a vector space A with a bilinear multiplication ′′ • ′′ such that the product [x, y] = x • y − y • x endows A with the structure of a Malcev algebra, and the left multiplication operator L • (x) : y → x • y define a representation of this Malcev algebra on A.…”