Moufang loops and generalized Lie-Cartan theorem

TL;DR

This paper extends the Lie-Cartan theorem to analytic Moufang loops, deriving the commutation relations of their birepresentations and explicitly describing the associated Lie algebra of the multiplication group.

Contribution

It introduces a generalized Lie-Cartan theorem for Moufang loops and explicitly characterizes the Lie algebra of their multiplication group.

Findings

Derived commutation relations for birepresentations.

Explicitly described the Lie algebra of the multiplication group.

Extended Lie-Cartan theorem to Moufang loops.

Abstract

Generalized Lie-Cartan theorem for linear birepresentations of an analytic Moufang loop is considered. The commutation relations of the generators of the birepresentation were found. In particular, the Lie algebra of the multiplication group of the birepresentation is explicitly given.