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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Cartan-decomposition subgroups of $\operatorname {SO}(2,n)$
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by Hee Oh and Dave Witte Morris PDF
Trans. Amer. Math. Soc. 356 (2004), 1-38 Request permission

Abstract:

For $G = \operatorname {SL} (3,\mathbb {R})$ and $G = \operatorname {SO}(2,n)$, we give explicit, practical conditions that determine whether or not a closed, connected subgroup $H$ of $G$ has the property that there exists a compact subset $C$ of $G$ with $CHC = G$. To do this, we fix a Cartan decomposition $G = K A^+ K$ of $G$, and then carry out an approximate calculation of $(KHK) \cap A^+$ for each closed, connected subgroup $H$ of $G$.
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Additional Information
  • Hee Oh
  • Affiliation: Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078
  • Address at time of publication: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
  • MR Author ID: 615083
  • Email: heeoh@math.princeton.edu
  • Dave Witte Morris
  • Affiliation: Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078
  • Address at time of publication: Department of Mathematics and Computer Science, University of Lethbridge, Lethbridge, Alberta, Canada T1K 3M4
  • Email: dwitte@math.okstate.edu, dmorris@cs.uleth.ca
  • Received by editor(s): February 4, 1999
  • Received by editor(s) in revised form: March 4, 1999, and November 6, 1999
  • Published electronically: August 25, 2003
  • © Copyright 2003 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 356 (2004), 1-38
  • MSC (2000): Primary 22E46; Secondary 20G20, 22E15, 57S20
  • DOI: https://doi.org/10.1090/S0002-9947-03-03428-7
  • MathSciNet review: 2020022