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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
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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.

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Keywords: <IMG WIDTH="22" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$G$">-structure, torsion free connection, prolongation, symmetric operator of Lie algebra
Article copyright: © Copyright 1983 American Mathematical Society