A family of Lie algebras not extendible to a family of Lie groups
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- by Don Coppersmith
- Proc. Amer. Math. Soc. 66 (1977), 365-366
- DOI: https://doi.org/10.1090/S0002-9939-1977-0457622-9
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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
- Adrien Douady and Michel Lazard, Espaces fibrés en algèbres de Lie et en groupes, Invent. Math. 1 (1966), 133–151 (French). MR 197622, DOI 10.1007/BF01389725 D. Coppersmith, Deformations of Lie groups and Lie algebras, Ph. D. Dissertation, Harvard Univ., 1977 (unpublished).
- G. Hochschild and G. D. Mostow, Cohomology of Lie groups, Illinois J. Math. 6 (1962), 367–401. MR 147577
Bibliographic Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 66 (1977), 365-366
- MSC: Primary 22E15
- DOI: https://doi.org/10.1090/S0002-9939-1977-0457622-9
- MathSciNet review: 0457622