Moufang loops and Lie algebras

TL;DR

This paper demonstrates how Lie algebras can be explicitly associated with analytic Moufang loops, connecting algebraic structures and laying groundwork for quantum Moufang loops.

Contribution

It provides an explicit construction linking Lie algebras to analytic Moufang loops, extending the algebraic framework.

Findings

Lie algebras associated with Moufang loops are explicitly constructed.

The commutation relations align with those from alternative algebra theory.

This work serves as a step towards quantum Moufang loops.

Abstract

It is explicitly shown how the Lie algebras can be associated with the analytic Moufang loops. The resulting Lie algebra commutation relations are well known from the theory of alternative algebras and can be seen as a preliminary step to quantum Moufang loops.