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A new proof of the  -condition for real rank one simple Lie algebras and their classification
Author(s):
Paolo
Ciatti
Journal:
Proc. Amer. Math. Soc.
133
(2005),
1611-1616.
MSC (2000):
Primary 17B20
Posted:
December 31, 2004
MathSciNet review:
2120265
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Abstract:
In this paper a new purely algebraic proof of the  -condition for the nilpotent Iwasawa algebras in real rank one simple Lie algebras is presented, yielding the classification of real rank one simple Lie algebras.
References:
-
- 1.
- P. Ciatti, A Clifford Algebra Approach to Simple Lie Algebras of Real Rank Two, I: The
 case, J. Lie Theory 10 (2000), 53-80. MR 1747689 (2001e:17011) - 2.
- M. Cowling, A. Dooley, A. Korányi, F. Ricci, H-type Groups and Iwasawa Decomposition, Adv. Math. 87, no. 1, (1991), 1-41. MR 1102963 (92e:22017)
- 3.
- M. Cowling, A. Dooley, A. Korányi, F. Ricci,, An Approach to Symmetric Spaces of Rank One via Groups of Heisenberg Type, J. Geom. Anal., 8, no. 2, (1998), 199-237.MR 1705176 (2000m:53071)
- 4.
- S. Helgason, Lie Groups, and Symmetric spaces, Academic Press, New York, 1978. MR 0514561 (80k:53081)
- 5.
- A. Kaplan, Fundamental Solutions for a Class of Hypoelliptic PDE Generated by Compositions of Quadratic Forms, Trans. Amer. Math. Soc. 258 (1980), 147-153.MR 0554324 (81c:58059)
- 6.
- A. Korányi, Geometric properties of Heisenberg-type Groups, Adv. Math. 56 (1985), 28-38.MR 0782541 (86h:53050)
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Additional Information:
Paolo
Ciatti
Affiliation:
Dipartimento Metodi e Modelli Matematici, Università di Padova, via Belzoni 7, Padova, Italy
Email:
ciatti@dmsa.unipd.it
DOI:
10.1090/S0002-9939-04-07725-1
PII:
S 0002-9939(04)07725-1
Received by editor(s):
January 3, 2001
Received by editor(s) in revised form:
September 24, 2001 and February 24, 2004
Posted:
December 31, 2004
Communicated by:
Dan M. Barbasch
Copyright of article:
Copyright
2004,
American Mathematical Society
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