On the interior of subsemigroups of Lie groups
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- by K. H. Hofmann and W. A. F. Ruppert PDF
- Trans. Amer. Math. Soc. 324 (1991), 169-179 Request permission
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
- Joachim Hilgert, Karl Heinrich Hofmann, and Jimmie D. Lawson, Lie groups, convex cones, and semigroups, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1989. Oxford Science Publications. MR 1032761
- K. H. Hofmann and W. A. F. Ruppert, The foliation of semigroups by congruence classes, Monatsh. Math. 106 (1988), no. 3, 179–204. MR 971922, DOI 10.1007/BF01318680
- Wolfgang A. F. Ruppert, On open subsemigroups of connected groups, Semigroup Forum 39 (1989), no. 3, 347–362. MR 1006403, DOI 10.1007/BF02573307
Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 324 (1991), 169-179
- MSC: Primary 22E99; Secondary 22A15
- DOI: https://doi.org/10.1090/S0002-9947-1991-0986692-6
- MathSciNet review: 986692