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Peer-reviewedCC BYMonatshefte fur Mathematik

Classification of quaternionic skew-Hermitian symmetric spaces.

  • Ioannis Chrysikos1
  • Jan Gregorovič2,3
  1. 1Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlářská 2, 611 37 Brno, Czech Republic.
  2. 2Department of Mathematics, Faculty of Science, University of Ostrava, 701 03 Ostrava, Czech Republic.
  3. 3Institute of Discrete Mathematics and Geometry, TU Vienna, Wiedner Hauptstrasse 8-10/104, 1040 Vienna, Austria.
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Abstract

We provide a complete classification of quaternionic skew-Hermitian symmetric spaces, namely symmetric spaces that admit a torsion-free SO∗(2n)Sp(1) -structure for arbitrary n>1 . Moreover, we prove that any homogeneous quaternionic skew-Hermitian manifold is necessarily a symmetric space.

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Cite

BibTeXRIS
BibTeX
@article{chrysikos2026classification,
  title = {{Classification of quaternionic skew-Hermitian symmetric spaces.}},
  author = {Ioannis Chrysikos and Jan Gregorovič},
  journal = {Monatshefte fur Mathematik},
  year = {2026},
  month = sep,
  doi = {10.1007/s00605-026-02225-y},
  url = {https://europepmc.org/article/MED/42999692},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Classification of quaternionic skew-Hermitian symmetric spaces.
AU  - Ioannis Chrysikos
AU  - Jan Gregorovič
PY  - 2026
DA  - 2026/09/30
JO  - Monatshefte fur Mathematik
DO  - 10.1007/s00605-026-02225-y
UR  - https://europepmc.org/article/MED/42999692
AB  - We provide a complete classification of quaternionic skew-Hermitian symmetric spaces, namely symmetric spaces that admit a torsion-free SO∗(2n)Sp(1) -structure for arbitrary n>1 . Moreover, we prove that any homogeneous quaternionic skew-Hermitian manifold is necessarily a symmetric space.
SN  - 0026-9255
SN  - 1436-5081
ER  -