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Algebraic structure of transsymmetric spaces. (English) Zbl 0972.20041
Costa, Roberto (ed.) et al., Nonassociative algebra and its applications. Proceedings of the fourth international conference, São Paulo, Brazil. New York, NY: Marcel Dekker (ISBN 978-0-8247-0406-3/pbk; 978-1-138-40176-1/hbk; 978-0-429-18767-4/ebook). Lect. Notes Pure Appl. Math. 211, 349-355 (2000).
Transsymmetric spaces have been introduced by L. V. Sabinin as a far going generalization of symmetric spaces, and studied by L. L. Sabinina [cf. On the geometry of smooth $$F$$-quasigroups, Ph.D. thesis, Friendship of Nations Univ. Moscow (1992)]. Despite of the geometric nature of the initial approach, in this paper the author studies a new reformulation in terms of smooth quasigroups and loops.
For the entire collection see [Zbl 0940.00027].
##### MSC:
 20N05 Loops, quasigroups 53C35 Differential geometry of symmetric spaces