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Extension of local loop isomorphisms

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Abstract

The paper contains the proof of the existence and uniqueness of the global extension of analytical local loop isomorphisms. The result is applied to the proof of the one-to-one correspondence between simply connected Moufang loops and Malcev algebras and to a global description of complete Moufang 3-webs.

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References

  1. Akivis, M. A., Selekhov, A. M.: Foundation of the Theory of Webs. Kalinin: Kalinin Gosuv. Univ. (1981).

    Google Scholar 

  2. Hofmann, K. H., Strambach, K.: Topological and analytical loops. In: The Theory of Quasigroups and Loops. (O. Chain, H. Pflugfelder andJ. Smith, Eds.) Berlin: Heldermann-Verlag.

  3. Kerdman, F. S.: Analytic Moufang loops in the large. Algebra i Logika18, 523–555 (1979).

    Google Scholar 

  4. Kobayashi, S., Nomizu, K.: Foundations of Differential Geometry, Vol. I. New York-London: Interscience. 1963.

    Google Scholar 

  5. Kuzmin, E. N.: On the connections between Malcev algebras and analytic Moufang loops. Algebra i Logika10, 3–22 (1971).

    Google Scholar 

  6. Malcev, I. A.: Analytical loops. Mat. Sb.36, 569–576 (1955).

    Google Scholar 

  7. Nagy, P. T.: Invariant tensor fields and the canonical connection of a 3-web. Aequationes Math.35, 31–44 (1988).

    Google Scholar 

  8. Nagy, P. T.: Complete group 3-webs and 3-nets. Arch. Math.53, 411–413 (1989).

    Google Scholar 

  9. Sagle, A. A.: Malcev algebras. Trans. Amer. Math. Soc.101, 426–458 (1961).

    Google Scholar 

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Nagy, P.T. Extension of local loop isomorphisms. Monatshefte für Mathematik 112, 221–225 (1991). https://doi.org/10.1007/BF01297341

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  • DOI: https://doi.org/10.1007/BF01297341

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