Journal of the Mathematical Society of Japan

The classification of real forms of simple irreducible pseudo-Hermitian symmetric spaces

Nobutaka BOUMUKI

Full-text: Open access

Abstract

The main purpose of this paper is to classify the real forms $M$ of simple irreducible pseudo-Hermitian symmetric spaces $G/R$ 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.

Article information

Source
J. Math. Soc. Japan, Volume 66, Number 1 (2014), 37-88.

Dates
First available in Project Euclid: 24 January 2014

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1390600836

Digital Object Identifier
doi:10.2969/jmsj/06610037

Mathematical Reviews number (MathSciNet)
MR3161392

Zentralblatt MATH identifier
1288.32031

Subjects
Primary: 32M15: Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras [See also 22E10, 22E40, 53C35, 57T15]
Secondary: 17B22: Root systems

Keywords
irreducible pseudo-Hermitian symmetric space real form simple para-Hermitian symmetric Lie algebra para-holomorphic involution

Citation

BOUMUKI, Nobutaka. The classification of real forms of simple irreducible pseudo-Hermitian symmetric spaces. J. Math. Soc. Japan 66 (2014), no. 1, 37--88. doi:10.2969/jmsj/06610037. https://projecteuclid.org/euclid.jmsj/1390600836


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