The project has been evolving since March 2010 into a semisimple Lie algebra online calculator
The calculator is still completely experimental (use at your own risk).Computations of vector partitions
The online computation of vector partition functions is down at the moment, will be restored, with an online interface only.
Developers
To join this project, contact Todor Milev, todor.milev at google's email.
The calculator page contains a non-tested description of how to try to install the calculator on your machine. Requires understanding of C++. You are cordially invited to use the source code however you wish (under the usual Library General Public License).
Computations with simple Lie algebras
The program has functions working with semisimple Lie algebras. For example it computes html tables with the root subsystems of simple root systems of rank<=8. Root subsystems parametrize the reductive root subalgebras of a simple Lie algebra (a root subalgebra is defined as a subalgebra containing a Cartan subalgebra). The calculator also includes tables with one representative of each conjugacy class of complex sl(2)-subalgebras of a simple Lie algebra, computed according to the algorithm described in Dynkin's paper "Semisimple Lie subalgebras of semisimple Lie algebras".
Here is a list of some of the structure theory of the semisimple subalgerbas of the simple Lie algebras of rank 8 or less as computed by the calculator.
The calculator also gives matrices of finite dimensional simple representations of simple complex Lie algebras. The dimension must be small enough, effectively up to around 200. For example, here is the 27 dimensional irreducible representation of the Lie algebra G_2 (to the left you will find an "info expand/collapse" button/link, there are the matrices giving of the Lie algebra G_2 action): hwv{}(G_2, (2,0),(0,0));
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A Root system visualization in javascript. Try projecting the root system of B3 (so(7)) onto G2! (hint: try to put the 1st and 3rd basis vector on top of one another).
Select root system.The basis vectors correspond to the vertices of the Dynkin diagram.
You can drag the center and the basis vectors.
The root system in simple basis coordinates follows.
Project Information
Acknowledgements. Many thanks to Thomas Bliem for setting up the SVN repository (August 2009)! Many thanks to the IT department of Jacobs Univesity for hosting the calculator software, as well as for setting up and supporting the Apache web server (March 2010)! Many thanks to Madan Chaudhary and his website for the javascript autocomplete code in the online calculator (August 2011)!
About this project:
This is the Vector partition function project ("vectorpartition")
This project was registered on SourceForge.net on May 21, 2009.
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