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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Lie groups locally isomorphic to generalized Heisenberg groups


Authors: Hiroshi Tamaru and Hisashi Yoshida
Journal: Proc. Amer. Math. Soc. 136 (2008), 3247-3254
MSC (2000): Primary 53C30; Secondary 22E25
Published electronically: April 22, 2008
MathSciNet review: 2407090
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Abstract: We classify connected Lie groups which are locally isomorphic to generalized Heisenberg groups. For a given generalized Heisenberg group $ N$, there is a one-to-one correspondence between the set of isomorphism classes of connected Lie groups which are locally isomorphic to $ N$ and a union of certain quotients of noncompact Riemannian symmetric spaces.


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Additional Information

Hiroshi Tamaru
Affiliation: Department of Mathematics, Hiroshima University, Higashi-Hiroshima 739-8526, Japan
Email: tamaru@math.sci.hiroshima-u.ac.jp

Hisashi Yoshida
Affiliation: Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09489-6
PII: S 0002-9939(08)09489-6
Keywords: Generalized Heisenberg groups, automorphism groups, local isomorphisms of Lie groups
Received by editor(s): October 11, 2006
Published electronically: April 22, 2008
Additional Notes: The first author was supported in part by Grant-in-Aid for Young Scientists (B) 17740039, The Ministry of Education, Culture, Sports, Science and Technology, Japan.
Communicated by: Dan M. Barbasch
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.