Programs in Physics & Physical Chemistry
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|Manuscript Title: The computer calculation of graded contractions of Lie algebras and their representations.|
|Authors: D. Berube, M. de Montigny|
|Program title: CONTRACTIONS|
|Catalogue identifier: ACNN_v1_0|
Distribution format: gz
|Journal reference: Comput. Phys. Commun. 76(1993)389|
|Programming language: C, Mathematica.|
|Operating system: UNIX (BSD/System V).|
|RAM: 1000K words|
|Word size: 32|
|Keywords: Symmetry groups, Lie algebras, Contractions, C language, Mathematica, Computer algebra.|
Nature of problem:
In physics, the contraction procedure appears as a formal way to relate the symmetry Lie groups (Lie algebras) of different physical systems, or theories. A new method for contracting Lie algebras, based on the preservation of some grading, was recently constructed. The contraction parameters introduced into the action of the elements of the Lie algebra must satisfy some system of quadratic equations in order to define a contraction of Lie algebra (or its representations). However, in practice such systems are often too large to be solved by hand. The results apply to any Lie algebra (and representations) having this grading structure.
When we take the grading group to be an abelian finite group, it consists either of a cyclic group or of a tensor product of cyclic groups. The program is different depending on the number of cyclic groups (or "grading degree") involved in this tensor product. A C program was created to generate automatically the required MATHEMATICA program. For a specific degree, the algorithm is translated into a MATHEMATICA program that performs the mathematically essential part: to generate and solve contractions defining equations. The C program is used to enter grading structure parameters and to generate the MATHEMATICA program for the desired grading degree.
The computer time grows rapidly with the number of defining equations to be solved. Time limits and available computer memory may cause restrictions.
The present MATHEMATICA program constitutes the first attempt to find by computer graded contractions of Lie algebras and their representations. The C-program generates the appropriate MATHEMATICA program. All the calculations are done in batch mode.
The running time increases rapidly with the grading group degree. Typical running times are given at the beginning of section 4.
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