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On the problem of universality of the identity of geometricity. (Russian) Zbl 0659.22003
Webs and quasigroups, Interuniv. thematic Collect. sci. Works, Kalinin 1988, 84-87 (1988).
[For the entire collection see Zbl 0632.00006.]
The identity of geometricity \((1)\quad l_{x,y}(ty)=tl_{x,y}(y)\) where \(l_{x,y}=L_{x,y^{-1}}L_ xL_ y\) and L is the operator of the right shift in the odule Q characterizes the right geometric odules [see L. V. Sabinin, Webs and quasigroups, Interuniv. thematic Collect. sci. Works, Kalinin 1987, 88-98 (1987; Zbl 0637.53014)]. However, isotopes of a geometric odule are not necessarily geometric odules, i.e. identity (1) does not turn into an equivalent identity under isotopy. In the paper under review a class of geometric odules is distinguished for which the identity (1) is preserved under isotopy.
Reviewer: V.Goldberg

MSC:
22A30 Other topological algebraic systems and their representations
20N05 Loops, quasigroups