2023Hiroshima Mathematical JournalOpen access

Para-real forms of para-Hermitian symmetric spaces and real forms of pseudo-Hermitian symmetric spaces

Kyoji Sugimoto

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Abstract

We show that each of the pseudo-Riemannian symmetric R-space associated with a non-degenerate Jordan triple system and a real form of an effective simple irreducible pseudo-Hermitian symmetric space can be realized as a para-real form of an effective semisimple para-Hermitian symmetric space of hyperbolic orbit type.

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We show that each of the pseudo-Riemannian symmetric R-space associated with a non-degenerate Jordan triple system and a real form of an effective simple irreducible pseudo-Hermitian symmetric space can be realized as a para-real form of an effective semisimple para-Hermitian symmetric space of hyperbolic orbit type.

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We show that each of the pseudo-Riemannian symmetric R-space associated with a non-degenerate Jordan triple system and a real form of an effective simple irreducible pseudo-Hermitian symmetric space can be realized as a para-real form of an effective semisimple para-Hermitian symmetric space of hyperbolic orbit type.

Key concepts: Triple system, Hermitian symmetric space, Hermitian matrix, Mathematics, Hermitian function, Symmetric space, Pure mathematics, Degenerate energy levels

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