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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
##### Keywords:
reductive space; left $$F$$-quasigroup