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

Coppersmith, Don

doi:10.1090/S0002-9939-1977-0457622-9

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A family of Lie algebras not extendible to a family of Lie groups
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Proc. Amer. Math. Soc. 66 (1977), 365-366 Request permission

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

Deformations of Lie groups and Lie algebras

G. Hochschild and G. D. Mostow, Cohomology of Lie groups, Illinois J. Math. 6 (1962), 367–401. MR 147577