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To the theory of generalized hyporeductive loops. (English) Zbl 0747.22001
Webs and quasigroups. (“Nonlinear geometric algebra-89”), Tver’, 156-163 (1991).
[For the entire collection see Zbl 0742.00044.]
A class of smooth left monoalternative loops is considered in which a complex identity holds. It is proved that a loop of this kind is hyporeductive and the right basic vector fields on it form a so-called hyporeductive algebra (see the definitions in a paper by L. V. Sabinin [ibid. 129-137 (1991; see the following review Zbl 0747.22002)]).
22A22 Topological groupoids (including differentiable and Lie groupoids)
53A60 Differential geometry of webs
20N05 Loops, quasigroups
22A30 Other topological algebraic systems and their representations