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On the theory of G-webs and G-loops. (English) Zbl 0745.53011
Global differential geometry and global analysis, Proc. Conf., Berlin/Ger. 1990, Lect. Notes Math. 1481, 264-270 (1991).
[For the entire collection see Zbl 0733.00014.]
$$G$$-loops are loops that admit a transitive group of automorphisms. Abstract $$G$$-loops were studied by many authors [see, for example, R. Bruck, A survey on binary systems (Berlin 1971; Zbl 0206.30301)]. The author finds local invariants of an analytic $$G$$-loop, gives interesting examples of $$G$$-loops and formulates the problem of construction of the general theory of $$G$$-loops. The $$G$$-loops are studied in the paper via the corresponding $$G$$-webs.

MSC:
 53A60 Differential geometry of webs 22A30 Other topological algebraic systems and their representations 20N05 Loops, quasigroups 17D99 Other nonassociative rings and algebras