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A Modular Algorithm for Computing Cohomologies of Lie Algebras and Superalgebras

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Abstract

The paper describes an improved algorithm for computing cohomologies of Lie (super)algebras. The original algorithm developed earlier by the author of this paper is based on the decomposition of the entire cochain complex into minimal subcomplexes. The suggested improvement consists in the replacement of the arithmetic of rational or integer numbers by a more efficient arithmetic of modular fields and the use of the relationship dim H k(\(\mathbb{F}\) p) ≥ dimH k(ℚ) between the dimensions of cohomologies over an arbitrary modular field \(\mathbb{F}\) p = ℤ/pℤ and the filed of rational numbers ℚ. This inequality allows us to rapidly find subcomplexes for which dimH k(\(\mathbb{F}\) p) > 0 (the number of such subcomplexes is usually not great) using computations over an arbitrary \(\mathbb{F}\) p and, then, carry out all required computations over ℚ in these subcomplexes.

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Authors and Affiliations

  1. Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna, Moscow oblast, 141980, Russia

    V. V. Kornyak

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  1. V. V. Kornyak
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Kornyak, V.V. A Modular Algorithm for Computing Cohomologies of Lie Algebras and Superalgebras. Programming and Computer Software 30, 157–163 (2004). https://doi.org/10.1023/B:PACS.0000029580.59590.ae

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  • DOI: https://doi.org/10.1023/B:PACS.0000029580.59590.ae

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