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Quasigroups of transformations. (English) Zbl 0812.22004
Lómus, J. (ed.) et al., Quasigroups and nonassociative algebras in physics. Papers from the seminar held in Tartu (USSR), June 12-17, 1989. Tartu: Institut Fiziki AN Ehstonii, Eesti Teaduste Akadeemia Füüsika Instituudi Uurimused. 66, 54-66 (1990).
Summary: The work deals with the families of transformations of a set (a smooth manifold) \(M\), which are not necessarily closed with respect to the composition law. In this case the system of notions of the theory of quasigroups and loops appears to be a natural working language, since the action of a family of transformations with regard to an arbitrary fixed point \(a\) of the set \(M\) can be described by a loop; loops associated with different points of the set \(M\) are isotopic to each other. The construction was meant for applications in geometry and mathematical physics.
For the entire collection see [Zbl 0788.00016].

22A30 Other topological algebraic systems and their representations
20N05 Loops, quasigroups
57S99 Topological transformation groups