Homogeneous spaces and quasigroups
The paper is a review dedicated to loops and homogeneous spaces. Let \(G/H\) be a homogeneous space, \(Q\) be a submanifold of the Lie group \(G\) through the unit of \(G\) transversal to the cosets \(gH\). Then we can define a binary operation on \(Q\) by projection on \(Q\) along the leaves \(gH\). Conversely, one can reconstruct a homogeneous space \(G/H\) from the given loop \(Q\). The connection between \(Q\) and \(G/H\) gives a possibility to describe the homogeneous space properties in terms of quasigroup and loop theory.
scientific article; zbMATH DE number 1023856