SYMMETRIC SPACES WITH DISSECTING INVOLUTIONS

Neeb KH, Ólafsson G (2020)

Publication Type: Journal article

Publication year: 2020

Journal

Transformation Groups Springer Verlag (Germany)

DOI: 10.1007/s00031-020-09595-z

Abstract

An involutive diffeomorphism σ of a connected smooth manifold M is called dissecting if the complement of its fixed point set is not connected. Dissecting involutions on a complete Riemannian manifold are closely related to constructive quantum field theory through the work of Dimock and Jaffe/Ritter on the construction of reflection positive Hilbert spaces. In this article we classify all pairs (M, σ), where M is an irreducible connected symmetric space, not necessarily Riemannian, and σ is a dissecting involutive automorphism. In particular, we show that the only irreducible, connected and simply connected Riemannian symmetric spaces with dissecting isometric involutions are Sn and ℍn, where the corresponding fixed point spaces are Sn−1 and ℍn − 1, respectively.

Authors with CRIS profile

Karl Hermann Neeb Lehrstuhl für Mathematik (Lie-Gruppen und Darstellungstheorie)

Involved external institutions

Louisiana State University US United States (USA) (US)

How to cite

APA:

Neeb, K.H., & Ólafsson, G. (2020). SYMMETRIC SPACES WITH DISSECTING INVOLUTIONS. Transformation Groups. https://dx.doi.org/10.1007/s00031-020-09595-z

MLA:

Neeb, Karl Hermann, and G. Ólafsson. "SYMMETRIC SPACES WITH DISSECTING INVOLUTIONS." Transformation Groups (2020).

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