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Lie Algebras
Author

Rolf Sulanke
Organization: Humboldt-University Berlin
Department: Mathematics
URL: http://www-irm.mathematik.hu-berlin.de/~sulanke
Old MathSource #

0210-845
Revision date

1999-11-24
Description

In the notebook and the packages we define basic operations for Lie algebras of matrices, and calculate the Killing forms of the following Lie algebras:
the general linear Lie algebras gl(n,K),
the special linear Lie algebras sl(n,K),
the orthogonal Lie algebras o(n),
the pseudo-orthogonal Lie algebras o(n, l),
the symplectic Lie algebras sp(2n, K),
the unitary Lie algebras u(n),
the special unitary Lie algebras su(n).
Here K denotes the fields of the real or the complex numbers. Furthermore we construct an orthonormalization procedure appropriate for arbitrary symmetric bilinear forms defined on spaces of matrices, in particular for Killing forms. By the help of this orthonormalization we calculate the index of the considered Killing forms (in the real case, for small values of n). In principle the tools submitted here give the possibility to perform any calculation in the series of Lie algebras listed above.
Subject

*Mathematics > Algebra > Group Theory
Keywords

Lie algebra, Killing form, orthogonalization in matrix spaces
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liealgeb.txt (3.7 KB) - Documentation
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Declare.m (8.2 KB) - Mathematica Package needed by liealgun.m
Download
lie.tgz (130 KB) - Lie Algebras tar file archive
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liealg.m (12.9 KB) - Mathematica Package
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liealgeb.nb (96.2 KB) - Example notebook for liealg.m, liealgun.m
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liealgun.m (4.5 KB) - Mathematica Package