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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Uniqueness of torsion free connection on some invariant structures on Lie groups
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by Michel Nguiffo Boyom and Georges Giraud PDF
Trans. Amer. Math. Soc. 280 (1983), 797-808 Request permission

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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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 280 (1983), 797-808
  • MSC: Primary 53C05
  • DOI: https://doi.org/10.1090/S0002-9947-1983-0716851-4
  • MathSciNet review: 716851