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Computation Of Cohomology Of Lie Superalgebras Of Vector Fields

Author

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  • V. V. KORNYAK

    (Laboratory of Computing Technique and Automation, Joint Institute for Nuclear Research, Dubna, Moscow region 141980, Russia)

Abstract

The cohomology of Lie (super)algebras has many important applications in mathematics and physics. It carries most fundamental ("topological") information about algebra under consideration. At present, because of the need for very tedious algebraic computation, the explicitly computed cohomology for different classes of Lie (super)algebras is known only in a few cases. That is why application of computer algebra methods is important for this problem. We describe here an algorithm and its C implementation for computing the cohomology of Lie algebras and superalgebras. The program can proceed finite-dimensional algebras and infinite-dimensional graded algebras with finite-dimensional homogeneous components. Among the last algebras, Lie algebras and superalgebras of formal vector fields are most important. We present some results of computation of cohomology for Lie superalgebras of Buttin vector fields and related algebras. These algebras being super-analogs of Poisson and Hamiltonian algebras have found many applications to modern supersymmetric models of theoretical and mathematical physics.

Suggested Citation

  • V. V. Kornyak, 2000. "Computation Of Cohomology Of Lie Superalgebras Of Vector Fields," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 11(02), pages 397-413.
    • Handle: RePEc:wsi:ijmpcx:v:11:y:2000:i:02:n:s0129183100000353
    DOI: 10.1142/S0129183100000353
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