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Computing in nilpotent Lie algebras


9 August 2022

Csaba Schneider
Departamento de Matemática
Instituto de Ciências Exatas
Universidade Federal de Minas Gerais (UFMG)
Belo Horizonte, Brasil


Sophus is a GAP4 package to compute with nilpotent Lie algebras over finite prime fields. In particular, the package can be used to compute certain central extensions and the automorphism group of such Lie algebras. Sophus also enables its user to test isomorphism between two nilpotent Lie algebras. The author of the package used it to construct all Lie algebras of dimension at most 9 over \(\mathbb F_2\).


© 2004, 2005 Csaba Schneider

The Sophus 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.


Most of the work on this package was carried out while I held a research position at the Technische Universität Braunschweig. I would like to express my gratitude to the staff and the students of the Institut für Geometrie for their interest in this work. Special thanks go to Bettina Eick for her rôle in completing this project.


1 The theory
2 A sample calculation with Sophus
3 Sophus functions

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