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Reductive spaces and left \(F\)-quasigroups. (English) Zbl 0746.53052
Webs and quasigroups. (“Nonlinear geometric algebra-89”), Tver’, 123-128 (1991).
[For the entire collection see Zbl 0742.00044.]
A left \(F\)-quasigroup \((M,\;\cdot,\;\backslash)\) with the identity \(x\cdot (y\cdot z)=(x\cdot y)\cdot(kx\cdot z)\), \(kx=x\backslash x\), is considered. A reductive space \(G/H\) connected with \(M\) is constructed. On \(G/H\) another left \(F\)-quasigroup (standard left \(F\)-quasigroup) is determined, which is isomorphic to the initial \(F\)-quasigroup \(M\).

MSC:
53C99 Global differential geometry
20N05 Loops, quasigroups
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