Journal of the Mathematical Society of Japan
Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645
The classification of real forms of simple irreducible pseudo-Hermitian symmetric spaces
Nobutaka Boumuki
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2014 年 66 巻 1 号 p. 37-88

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The main purpose of this paper is to classify the real forms M of simple irreducible pseudo-Hermitian symmetric spaces GR with G non-compact. That provides an extension of Jaffee's results (Bull. Amer. Math. Soc. '75; J. Differential Geom. '78), Leung's result (J. Differential Geom. '79) and Takeuchi's result (Tohoku Math. J. '84) concerning the classification of real forms of irreducible Hermitian symmetric spaces of the non-compact type. Moreover, that enables us to classify the pairs of simple para-Hermitian symmetric Lie algebras and their para-holomorphic involutions, which includes Kaneyuki-Kozai's result (Tokyo J. Math. '85) of the classification of simple para-Hermitian symmetric Lie algebras.
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