Note on analytic Moufang loops

Eugen Paal

Commentationes Mathematicae Universitatis Carolinae (2004)

  • Volume: 45, Issue: 2, page 349-354
  • ISSN: 0010-2628

Abstract

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It is explicitly shown how the Lie algebras can be associated with the analytic Moufang loops. The resulting Lie algebra commutation relations are well known from the theory of alternative algebras.

How to cite

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Paal, Eugen. "Note on analytic Moufang loops." Commentationes Mathematicae Universitatis Carolinae 45.2 (2004): 349-354. <http://eudml.org/doc/249351>.

@article{Paal2004,
abstract = {It is explicitly shown how the Lie algebras can be associated with the analytic Moufang loops. The resulting Lie algebra commutation relations are well known from the theory of alternative algebras.},
author = {Paal, Eugen},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Moufang loop; Mal'tsev algebra; generalized Maurer-Cartan equations; triality; analytic Moufang loops; Mal'tsev algebras; generalized Maurer-Cartan equations; triality},
language = {eng},
number = {2},
pages = {349-354},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Note on analytic Moufang loops},
url = {http://eudml.org/doc/249351},
volume = {45},
year = {2004},
}

TY - JOUR
AU - Paal, Eugen
TI - Note on analytic Moufang loops
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2004
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 45
IS - 2
SP - 349
EP - 354
AB - It is explicitly shown how the Lie algebras can be associated with the analytic Moufang loops. The resulting Lie algebra commutation relations are well known from the theory of alternative algebras.
LA - eng
KW - Moufang loop; Mal'tsev algebra; generalized Maurer-Cartan equations; triality; analytic Moufang loops; Mal'tsev algebras; generalized Maurer-Cartan equations; triality
UR - http://eudml.org/doc/249351
ER -

References

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  1. Moufang R., Zur Struktur von Alternativkörpern, Math. Ann. B110 (1935), 416-430. (1935) MR1512948
  2. Pflugfelder H., Quasigroups and Loops: Introduction, Heldermann Verlag Berlin (1990). (1990) Zbl0715.20043MR1125767
  3. Mal'tsev A.I., Analytic loops, Matem. Sb. 36 (1955), 569-576 (in Russian). (1955) MR0069190
  4. Paal E., An Introduction to Moufang Symmetry, Preprint F-42 Institute of Physics, Tartu (1987 (in Russian)). (1987 (in Russian)) MR1241991
  5. Loos O., Über eine Beziehung zwischen Malcev-Algebren und Lie-Tripelsystemen, Pacific J. Math. 18 (1966), 553-562. (1966) Zbl0145.04202MR0199236
  6. Yamaguti K., Note on Malcev algebras, Kumamoto J. Sci. A5 (1962), 203-207. (1962) Zbl0166.04203MR0158911
  7. Yamaguti Y., On the theory of Malcev algebras, Kumamoto J. Sci. A6 (1963), 9-45. (1963) Zbl0138.26203MR0167507
  8. Schafer R.D., An Introduction to Nonassociative Algebras, Academic Press New York (1966). (1966) Zbl0145.25601MR0210757

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