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Algebra and Logic

, Volume 47, Issue 5, pp 321–329 | Cite as

Special polynomials in free framed Lie algebra

  • A. V. GavriliovEmail author
Article
  • 16 Downloads

A framed Lie algebra is an algebra with two operations which is a Lie algebra with respect to one of these operations. A basic example is a Lie algebra of vector fields on a manifold with connection where the covariant derivative serves as an additional operation. In a free framed Lie algebra, we distinguish a set of special polynomials that geometrically correspond to invariantly defined tensors. A necessary condition of being special is derived, and we presume that this condition is also sufficient.

Keywords

nonassociative algebra Lie algebra affine connection 

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References

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    A. V. Gavriliov, “Algebraic properties of the covariant differentiation and composition of exponential mappings,” Mat. Tr., 9, No. 1, 3–20 (2006).MathSciNetGoogle Scholar
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    Sh. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Vols. 1, 2, Interscience, New York (1963, 1969).zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  1. 1.Institute of Computational Mathematics and Mathematical Geophysics, Siberian BranchRussian Academy of SciencesNovosibirskRussia

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