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- W965931176 abstract "A geodetikus loopok alapvető modellkent szolgalnak a differencialhato loopok elmeleteben. Vizsgaljuk a geodetikusokkal kapcsolatos differencialgeometriai strukturakat, a tanulmanyozott modszereket pedig alkalmaztuk a differencialhato loopok elmeleteben. A valos egyenesen ertelmezett olyan loopokra, amelyek baleltolasai altal generalt csoportja Lie-csoport, specialis koordinatarendszereket vezettunk be es meghataroztuk ezekben a szorzasművelet explicit előallitasat. A differencialgeometriabol es Lie-csoportok elmeleteből altalanositottuk a kanonikus koordinatarendszer fogalmat, ezekben felirt szorzasfuggveny segitsegevel meghataroztuk a vizsgalt loopok normalformajat es osztalyoztuk a vizsgalt loopok az izomorfia tipusait. Elvegeztuk a loopok bővites elmeletenek absztrakt szinten valo kiepiteset, sok peldaval illusztralva azt, hogy csoportok csoportokkal valo bővitesekent sok klasszikus gyenge asszociativitasi feltetelnek eleget tevő loop konstrualhato. | The geodesic loops give a basic model for the theory of differentiable loops. We investigated differential geometric structures which are connected with geodesics of manifolds and the methods are appplied in the theory of differentiable loops. Special coordinate systems are introduced for one-dimensional loops having a Lie group as the group generated by the left translations and an explicit form of the multiplication function is determined. The notion of canonical coordinate system of differential geometry and Lie group theory is generalized to differentiable loops, the multiplication function defined in canonical coordinate system gives the normalform of the loop multiplication. The isomorphism classes of the investigated loops are determined. We developed the extension theory of abstract loops and showed with many examples that extensions of groups by groups gives poosibilities of construction of loops satisfying different classical weak associativity conditions." @default.
- W965931176 created "2016-06-24" @default.
- W965931176 creator A5003002235 @default.
- W965931176 date "2007-01-01" @default.
- W965931176 modified "2023-09-23" @default.
- W965931176 title "Geodetikus loopok Lie elmélete = Lie theory geodesic loops" @default.
- W965931176 hasPublicationYear "2007" @default.
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