Generalized symplectic symmetric spaces

TL;DR

This paper explores the generalization of symmetric symplectic spaces, extending Bieliavsky's work, and classifies all 3-symmetric symplectic spaces, contributing to the understanding of symplectic geometry in symmetric contexts.

Contribution

It constructs generalized symplectic symmetric spaces and provides a classification of all 3-symmetric symplectic spaces, expanding the theory beyond Bieliavsky's original framework.

Findings

Extended Bieliavsky's results to broader classes of symmetric spaces

Classified all 3-symmetric symplectic spaces

Provided new insights into symplectic geometry in symmetric settings

Abstract

Bielavsky introduced and investigated the class of symmetric symplectic spaces, that is, symmetric spaces endowed with a symplectic form invariant with respect to symmetries. Since the theory of symmetric spaces has generalizations, we ask a question about their possible symplectic versions. We do construct such generalizations and extend some of Bieliavsky's results. In particular, we classify all 3-symmetric symplectic spaces.