2003/05/31 by Vladimir V. Kornyak
Mathematics · Physics and Astronomy · #math.RT #math-ph #math.MP
published as Computer Algebra in Scientific Computing, V.G.Ganzha, E.W.Mayr and E.V.Vorozhtsov (Eds.), TUM, Munich, 2003, pp.227-240 · corrected to match published version
arxiv created 2003/09/30 · arxiv updated 2009/11/30
We describe an essential improvement of our recent algorithm for computing cohomology of Lie (super)algebra based on partition of the whole cochain complex into minimal subcomplexes. We replace the arithmetic of rational numbers or integers by a much cheaper arithmetic of a modular field and use the inequality between the dimensions of cohomology H over any modular field Fp = Z/pZ and over Q: dim H(Fp) >= dim H(Q). With this inequality we can, by computing over arbitrary Fp, quickly find the (usually, rare) subcomplexes for which dim H(Fp) > 0 and then carry out the full computation over Q within these subcomplexes. We also present the results of application of the corresponding C program to the Lie superalgebra of special vector fields preserving an "odd-symplectic" structure on the (2|2)-dimensional supermanifold. For this algebra, we found some new basis elements of the cohomology in the trivial module.