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Transactions of the American Mathematical Society

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



On the interior of subsemigroups of Lie groups

Authors: K. H. Hofmann and W. A. F. Ruppert
Journal: Trans. Amer. Math. Soc. 324 (1991), 169-179
MSC: Primary 22E99; Secondary 22A15
MathSciNet review: 986692
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Abstract: Let $ G$ denote a Lie group with Lie algebra $ \mathfrak{g}$ and with a subsemigroup $ S$ whose infinitesimal generators generate $ \mathfrak{g}$. We construct real analytic curves $ \gamma :{{\mathbf{R}}^ + } \to S$ such that $ \dot \gamma (0)$ is a preassigned tangent vector of $ S$ at the origin and that $ \gamma(t)$ is in the interior of $ S$ for all positive $ t$. Among the consequences, we find that the boundary of $ S$ has to be reasonably well behaved. Our procedure involves the construction of certain linear generating sets from a given Lie algebra generating set, and this may be of independent interest.

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

  • [1] J. Hilbert, K. H. Hofmann, and J. D. Lawson, Lie groups, convex cones, and semigroups, Oxford Univ. Press, 1989. MR 1032761 (91k:22020)
  • [2] K. H. Hofmann and W. A. F. Ruppert, On foliations induced by congruences, Monatsh. Math. 106 (1988), 179-204. MR 971922 (89i:22003)
  • [3] W. A. F. Ruppert, On open subsemigroups of Lie groups, Semigroup Forum 39 (1989), 347-362 (to appear). MR 1006403 (90g:22003)

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Keywords: Lie group, infinitesimally generated semigroup, analytic curve, analytic deformation, boundary
Article copyright: © Copyright 1991 American Mathematical Society

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