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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A family of Lie algebras not extendible to a family of Lie groups

Author: Don Coppersmith
Journal: Proc. Amer. Math. Soc. 66 (1977), 365-366
MSC: Primary 22E15
MathSciNet review: 0457622
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Abstract: We produce an analytic family of finite-dimensional Lie algebras, parameterized by a smooth Hausdorff manifold, which does not correspond to the Lie algebra of any Hausdorff (separable) family of Lie groups. This answers a question of Douady and Lazard.

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

  • [1] A. Douady and M. Lazard, Espaces fibrés en algèbres de Lie et en groupes, Invent. Math. 1 (1966), 133-151. MR 0197622 (33:5787)
  • [2] D. Coppersmith, Deformations of Lie groups and Lie algebras, Ph. D. Dissertation, Harvard Univ., 1977 (unpublished).
  • [3] G. Hochschild and G. D. Mostow, Cohomology of Lie groups, Illinois J. Math. 6 (1962), 367-401. MR 0147577 (26:5092)

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Article copyright: © Copyright 1977 American Mathematical Society

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