Abstract
A new algorithmic approach for computing cohomologies of Lie (super)algebras is described. This approach is based on splitting a complete cochain complex into minimal (in some noninvariant sense) subcomplexes; this makes the computations much more efficient due to the fact that the proposed splitting allows the cochain complex spaces (which, normally, have very large dimensions) to be decomposed into much smaller subspaces. The algorithms in a pseudocode are presented. The approach is illustrated by comprehensive examples.
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Fuks, D.B., Kogomologii beskonechnomernykh algebr Li (Cohomology of Infinite-Dimensional Lie Algebras), Moscow: Nauka, 1984.
Kornyak, V.V., A Program for Computing Cohomology of Lie Superalgebras of Vector Fields, Zap. Nauchn. Seminarov POMI (St. Petersburg), 1999, vol. 258, pp. 148–160.
Kornyak, V.V., Cohomology of Lie Superalgebras of Hamiltonian Vector Fields: Computer Analysis, Computer Algebra in Scientific Computing, Ganzha, V.G., Mayr, E.W., and Vorozhtsov, E.V., Eds., Berlin: Springer, 1999, pp. 241–249. http://arXiv.org/math.SC/9906046.
Kornyak, V.V., Computation of Cohomology of Lie Superalgebras of Vector Fields, Int. J. Modern Phys. C, 2000, vol. 11, no. 2, pp. 397–414. http://arXiv.org/math.SC/0002210.
Kornyak, V.V., Computation of Cohomology of Lie Superalgebras: Algorithm and Implementation, Programmirovanie, 2001, no. 3, pp. 46–50.
Gelfand, I.M., Kalinin, D.I., and Fuks, D.B., On Cohomologies of Lie Algebras of Hamiltonian Formal Vector Fields, Funkts. Anal. Ego Prilozh., 1972, vol. 6, pp. 25–29.
Perchik, J., Cohomology of Hamiltonian and Related Formal Vector Fields Lie Algebras, Topology, 1976, vol. 15, no. 4, pp. 395–404.
Guillemin, V.M. and Shnider, S.D., Some Stable Results on the Cohomology of Classical Infinite Dimensional Lie Algebras, Trans. Amer. Math. Soc., 1973, vol. 179, pp. 275–280.
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Kornyak, V.V. A Method of Splitting Cochain Complexes to Compute Cohomologies of Lie (Super)algebras. Programming and Computer Software 28, 76–80 (2002). https://doi.org/10.1023/A:1014872716962
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DOI: https://doi.org/10.1023/A:1014872716962