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Transactions of the American Mathematical Society

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Uniqueness of torsion free connection on some invariant structures on Lie groups


Authors: Michel Nguiffo Boyom and Georges Giraud
Journal: Trans. Amer. Math. Soc. 280 (1983), 797-808
MSC: Primary 53C05
MathSciNet review: 716851
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Abstract: Let $ \mathcal{G}$ be a connected Lie group with Lie algebra $ \mathfrak{g}$. Let $ \operatorname{Int}(\mathfrak{g})$ be the group of inner automorphisms of $ \mathfrak{g}$. The group $ \mathcal{G}$ is naturally equipped with $ \operatorname{Int}(\mathfrak{g})$-reductions of the bundle of linear frames on $ \mathcal{G}$. We investigate for what kind of Lie group the 0-connection of E. Cartan is the unique torsion free connection adapted to any of those $ \operatorname{Int}(\mathfrak{g})$-reductions.


References [Enhancements On Off] (What's this?)

  • [1] Victor Guillemin, A Jordan-Hölder decomposition for a certain class of infinite dimensional Lie algebras, J. Differential Geometry 2 (1968), 313–345. MR 0263882
  • [2] Nathan Jacobson, Lie algebras, Interscience Tracts in Pure and Applied Mathematics, No. 10, Interscience Publishers (a division of John Wiley & Sons), New York-London, 1962. MR 0143793
  • [3] John Milnor, Curvatures of left invariant metrics on Lie groups, Advances in Math. 21 (1976), no. 3, 293–329. MR 0425012
  • [4] I. M. Singer and Shlomo Sternberg, The infinite groups of Lie and Cartan. I. The transitive groups, J. Analyse Math. 15 (1965), 1–114. MR 0217822

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1983-0716851-4
Keywords: $ G$-structure, torsion free connection, prolongation, symmetric operator of Lie algebra
Article copyright: © Copyright 1983 American Mathematical Society