Symmetric Spaces of Noncompact type

Martin Moskowitz mmoskowi@mat.uniroma2.it

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Abstract

This article gives a detailed introduction to symmetric spaces of non-compact type and their relation to corresponding semisimple lie groups. This is done more or less from scratch and explicitely without the reader having to know large parts of modern differential geometry

Keywords

Semisimple Lie group and Lie algebra of non-compact type , Maximal compact subgroup and maximal subalgebra of compact type and their conjugacy. Cartan and polar decomposition , rank , irreducible symmetric space , isometry group , Killing form , exponential map , Cartan involution , law of cosines , two point homogeneous space

Martin Moskowitz Department of Mathematics, CUNY Graduate Center 365 Fifth Ave. New York NY 10016. USA.

Pages: 111 - 138
Date Published: 2005-08-01
Vol. 7 No. 2 (2005): CUBO, A Mathematical Journal

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Published

2005-08-01

How to Cite

[1]

M. Moskowitz, “Symmetric Spaces of Noncompact type”, CUBO, vol. 7, no. 2, pp. 111–138, Aug. 2005.

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Vol. 7 No. 2 (2005): CUBO, A Mathematical Journal

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Articles

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Roberto Dieci, Gian-Italo Bishi, Laura Gardini, Routes to Complexity in a Macroeconomic Model Described by a Noninvertible Triangular Map , CUBO, A Mathematical Journal: Vol. 5 No. 3 (2003): CUBO, Matemática Educacional
Rodolfo Baeza, On nuclear Bernstein algebras , CUBO, A Mathematical Journal: No. 6 (1990): CUBO, Revista de Matemática
M.I. Belishev, A.F. Vakulenko, On algebraic and uniqueness properties of harmonic quaternion fields on 3d manifolds , CUBO, A Mathematical Journal: Vol. 21 No. 1 (2019)
P. Brückmann, Tensor Differential Forms and Some Birational Invariants of Projective Manifolds , CUBO, A Mathematical Journal: Vol. 7 No. 1 (2005): CUBO, A Mathematical Journal
Philip J. Maher, Mohammad Sal Moslehian, More on approximate operators , CUBO, A Mathematical Journal: Vol. 14 No. 1 (2012): CUBO, A Mathematical Journal
Naoyuki Koike, Mean curvature flow of certain kind of isoparametric foliations on non-compact symmetric spaces , CUBO, A Mathematical Journal: Vol. 20 No. 3 (2018)
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Nafaa Chbili, Sym´etries en Dimension Trois: Une Approche Quantique , CUBO, A Mathematical Journal: Vol. 6 No. 4 (2004): CUBO, A Mathematical Journal
Mohadeseh Rostamani, Shirin Hejazian, Maps preserving Fredholm or semi-Fredholm elements relative to some ideal , CUBO, A Mathematical Journal: Vol. 17 No. 1 (2015): CUBO, A Mathematical Journal
Sehie Park, Remarks on KKM Maps and Fixed Point Theorems in Generalized Convex Spaces , CUBO, A Mathematical Journal: Vol. 10 No. 4 (2008): CUBO, A Mathematical Journal

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You may also start an advanced similarity search for this article.