Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 53C05

Retrieve articles in all journals with MSC: 53C05

Additional Information

Keywords: $ G$-structure, torsion free connection, prolongation, symmetric operator of Lie algebra
Article copyright: © Copyright 1983 American Mathematical Society