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Remarks on canonical connections of loops with the left inverse property. (English) Zbl 0625.53047
In his previous paper [see ibid. 19, 37-55 (1985; Zbl 0588.53014)] the author established some properties of the torsion and curvature tensors of the canonical affine connection of a homogeneous Lie loop at the unit element. In the paper under review he discovers the fact that the most of those properties are valid for the torsion and curvature tensors of the canonical affine connection of a differentiable loop G with the left inverse property, i.e. for a loop G for which each element x has a unique inverse \(x^{-1}\), \(x^{-1}x=xx^{-1}=e\) such that \(L_{x^{- 1}}=L_ x^{-1}\) where \(L_ x\) is the left translation by x.
Reviewer: V.V.Goldberg

MSC:
53C30 Differential geometry of homogeneous manifolds
22E99 Lie groups
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