Computing with real Lie Groups

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CoReLG

CoReLG is a GAP package for computing with finite dimensional real Lie algebras; it has been written for GAP version 4.5. CoReLG requires the latest version of the package SLA; once this package is installed, it will be loaded automatically when starting CoReLG. Please see the manual for more information and a detailed description. The official GAP website of CoReLG can be found here.

Installation

The installation follows standard GAP rules. So the normal way to install is to unpack the archive in the `pkg' directory, which will create a subdirectory `corelg'. The package and documentation are now maintained via Github:

• Git Hub Link: corelg

  Theoretical background and further information

  The underlying theory is to some extent described in the manual; see also the following publications.
  • A computational approach to the Kostant-Sekiguchi correspondence.
    Heiko Dietrich and Willem de Graaf.
    Pacific J. Mathematics 265 (2), 349 - 379 (2013).
  • Computing with real Lie algebras: real forms, Cartan decompositions, and Cartan subalgebras.
    Heiko Dietrich, Paolo Faccin, and Willem A. de Graaf.
    J. Symb. Computation 56, 27 - 45 (2013).
  • A GAP package for computing with real semisimple Lie algebras.
    Heiko Dietrich, Paolo Faccin, and Willem A. de Graaf.
    in H. Hong and C. Yap (Eds.): ICMS 2014, LNCS 8592, pp. 59 - 66. Springer (2014).
  • Regular subalgebras and nilpotent orbits of real graded Lie algebras.
    Heiko Dietrich, Paolo Faccin, and Willem A. de Graaf.
    J. Algebra 423, 1044 - 1079 (2015).
  • Nilpotent orbits in real symmetric pairs and stationary black holes.
    Heiko Dietrich, Willem A. de Graaf, Daniele Ruggeri, and Mario Trigiante.
    Fortschr. Phys. 65, 2, 1600118 (2017).
  
  

  Authors

  Heiko Dietrich School of Mathematics Monash University Wellington Road 1 VIC 3800, Melbourne Australia

  Paolo Faccin Department of Mathematics University of Trento Via Sommarive 14 I-38050 Povo (Trento) Italy

  Willem de Graaf Department of Mathematics University of Trento Via Sommarive 14 I-38050 Povo (Trento) Italy

  
  

  Acknowledgements

  The research for this package was supported by funding from the European Union's Seventh Framework Program FP7/2007-2013, grant agreement no 271712 (2011-2013) and by an ARC DP grant (2019-2021), identifier DP190100317. Dietrich was supported by an ARC DECRA Fellowship, project DE140100088 (2014-2016).
  
  

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