Nonexistence of standard compact Clifford–Klein forms of homogeneous spaces of exceptional Lie groups
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- by Maciej Bocheński, Piotr Jastrzȩbski and Aleksy Tralle HTML | PDF
- Math. Comp. 89 (2020), 1487-1499 Request permission
Abstract:
We use a computer-aided approach to prove that there are no standard compact Clifford–Klein forms of homogeneous spaces of exceptional Lie groups. This yields further support for Kobayashi’s conjecture about possible compact Clifford–Klein forms. Our approach is based on the algorithms developed in this work. They are inspired by the algorithmic methods of classifying semisimple subalgebras in simple Lie algebras developed by Faccin and de Graaf. Also, we use the databases created by them. These algorithms eliminate the majority of possibilities. We complete the proof using Kobayashi’s criterion for properness of the Lie group action.References
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Additional Information
- Maciej Bocheński
- Affiliation: Faculty of Mathematics and Computer Science, University of Warmia and Mazury, Słoneczna 54, 10-710 Olsztyn, Poland
- MR Author ID: 1069305
- Email: mabo@matman.uwm.edu.pl
- Piotr Jastrzȩbski
- Affiliation: Faculty of Mathematics and Computer Science, University of Warmia and Mazury, Słoneczna 54, 10-710 Olsztyn, Poland
- Email: piojas@matman.uwm.edu.pl
- Aleksy Tralle
- Affiliation: Faculty of Mathematics and Computer Science, University of Warmia and Mazury, Słoneczna 54, 10-710 Olsztyn, Poland
- MR Author ID: 199440
- Email: tralle@matman.uwm.edu.pl
- Received by editor(s): January 14, 2019
- Received by editor(s) in revised form: July 1, 2019, and July 28, 2019
- Published electronically: November 26, 2019
- Additional Notes: The first author acknowledges the support of the National Science Center (grant NCN no. 2018/31/D/ST1/00083).
The third author acknowledges the support of the National Science Center (grant NCN no. 2018/31/B/ST1/00053). - © Copyright 2019 American Mathematical Society
- Journal: Math. Comp. 89 (2020), 1487-1499
- MSC (2010): Primary 57S30, 17B20, 22F30, 22E40, 65-05, 65FXX
- DOI: https://doi.org/10.1090/mcom/3493
- MathSciNet review: 4063325