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# NoCK

## Computing obstruction for the existence of compact Clifford-Klein form

1.5

30 March 2022

Maciej Bocheński
Email: mabo@matman.uwm.edu.pl

Piotr Jastrzębski
Email: piojas@matman.uwm.edu.pl
Homepage: http://wmii.uwm.edu.pl/~piojas/

Anna Szczepkowska
Email: anna.szczepkowska@matman.uwm.edu.pl

Aleksy Tralle
Email: tralle@matman.uwm.edu.pl
Homepage: http://wmii.uwm.edu.pl/~tralle/

Artur Woike
Email: awoike@matman.uwm.edu.pl
Homepage: http://wmii.uwm.edu.pl/~awoike

### Abstract

In this package we develop functions for an algorithm designed to find homogeneous spaces of semisimple non-compact Lie groups which do not admit compact Clifford-Klein forms.

### Copyright

NoCK Package is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

### Acknowledgements

We thank Willem de Graaf for his help in getting some literature sources.

### Contents

1 Notation
2 Obstruction for the existence of compact Clifford-Klein form
2.1 Technical functions
2.1-1 NonCompactDimension
2.1-2 PCoefficients
2.1-3 PCalculate
2.1-4 AllZeroDH
3 Algorithm example
References
Index
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