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Generalized Bol loops. (English) Zbl 0964.22017
The study of different kinds of group concept generalizations, in particular of Lie group concept generalizations, is an actual problem, since such objects arise in a natural way in geometry and mathematical physics. The smooth Bol loops and generalized Bol loops associated with symmetric spaces are the nearest ones to Lie groups. The authors study algebraic properties of generalized Bol loops. In particular, sufficient conditions are presented for generalized Bol loops to be Bol loops. Differential equations of generalized Bol loops are derived.
22E55 Representations of Lie and linear algebraic groups over global fields and adèle rings
22E67 Loop groups and related constructions, group-theoretic treatment