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Transsymmetric spaces. New results. (English) Zbl 0947.20054
Kolář, Ivan (ed.) et al., Differential geometry and applications. Proceedings of the 7th international conference, DGA 98, and satellite conference of ICM in Berlin, Brno, Czech Republic, August 10-14, 1998. Brno: Masaryk University. 437-442 (1999).
After necessary preliminaries on transsymmetric spaces [see L. V. Sabinin, L. L. Sabinina and the author, Publ. Math. 54, No. 3-4, 303-311 (1999)], the author announces a number of new results on perfect transsymmetric spaces. The most interesting of them is that any geodesic loop of a perfect transsymmetric space is a left Bol loop. Other results give a complete description of perfect transsymmetric spaces as reductive spaces in terms of Lie algebras.
For the entire collection see [Zbl 0923.00021].
20N05 Loops, quasigroups
53C35 Differential geometry of symmetric spaces
22A30 Other topological algebraic systems and their representations
14M17 Homogeneous spaces and generalizations
17D99 Other nonassociative rings and algebras
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