Deformations of Lie subgroups
HTML articles powered by AMS MathViewer
- by Don Coppersmith PDF
- Trans. Amer. Math. Soc. 233 (1977), 355-366 Request permission
Abstract:
We give rigidity and universality theorems for embedded deformations of Lie subgroups. If $K \subset H \subset G$ are Lie groups, with ${H^1}(K,g/h) = 0$, then for every ${C^\infty }$ deformation of H, a conjugate of K lies in each nearby fiber ${H_s}$. If $H \subset G$ with ${H^2}(H,g/h) = 0$, then there is a universal “weak” analytic deformation of H, whose base space is a manifold with tangent plane canonically identified with $\operatorname {Ker} {\delta ^1}$.References
- M. Artin, On the solutions of analytic equations, Invent. Math. 5 (1968), 277–291. MR 232018, DOI 10.1007/BF01389777
- 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
- G. Hochschild and G. D. Mostow, Cohomology of Lie groups, Illinois J. Math. 6 (1962), 367–401. MR 147577, DOI 10.1215/ijm/1255632500
- R. W. Richardson Jr., Deformations of Lie subgroups and the variation of isotropy subgroups, Acta Math. 129 (1972), 35–73. MR 299723, DOI 10.1007/BF02392213
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 233 (1977), 355-366
- MSC: Primary 22E15
- DOI: https://doi.org/10.1090/S0002-9947-1977-0457621-1
- MathSciNet review: 0457621