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Title: Bol loop actions (English)
Author: Sbitneva, Larissa
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 41
Issue: 2
Year: 2000
Pages: 405-408
Category: math
Summary: The notions of left Bol and Bol-Bruck actions are introduced. A purely algebraic analogue of a Nono family (Lie triple family), the so called Sabinin-Nono family, is given. It is shown that any Sabinin-Nono family is a left Bol-Bruck action. Finally it is proved that any local Nono family is a local left Bol-Bruck action. On general matters see [L.V. Sabinin 91, 99]. (English)
Keyword: Bol loop action
Keyword: Lie triple family
Keyword: Nono family
MSC: 20N05
MSC: 22A22
MSC: 53A60
idZBL: Zbl 1082.20507
idMR: MR1780881
Date available: 2009-01-08T19:02:45Z
Last updated: 2012-04-30
Stable URL:
Reference: [61] : Sur les familles triples locales de transformations locales de Lie.J. Sci. Hiroshima Univ., Ser. A-I Math. 25 (1961), 357-366 MR 28 (1964) #2174b. Zbl 0113.15801, MR 0158953
Reference: [91] : Analytic Quasigroups and Geometry (Russian).Monograph Friendship of Nations University Press Moscow (1991), 112 pp. MR 1284471
Reference: [99] : Smooth Quasigroups and Loops.Kluwer Academic Publishers Dordrecht, The Netherlands (1999), xvi + 249 pp. Zbl 0939.20064, MR 1727714


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