Computation of Cohomology of Lie Algebra of Hamiltonian Vector Fields by Splitting Cochain Complex into Minimal Subcomplexes

Details Computation of Cohomology of Lie Algebra of Hamiltonian Vector Fields by Splitting Cochain Complex into Minimal Subcomplexes Computation of Cohomology of Lie Algebra of Hamiltonian Vector Fields by Splitting Cochain Complex into Minimal Subcomplexes

2002-05-06

arxiv.org/abs/math/0205046v1

Mathematics

Numerical Analysis

8 pages, submitted to CASC-2002

Scientific paper

Computation of homology or cohomology is intrinsically a problem of high combinatorial complexity. Recently we proposed a new efficient algorithm for computing cohomologies of Lie algebras and superalgebras. This algorithm is based on partition of the full cochain complex into minimal subcomplexes. The algorithm was implemented as a C program LieCohomology. In this paper we present results of applying the program LieCohomology to the algebra of hamiltonian vector fields H(2|0). We demonstrate that the new approach is much more efficient comparing with the straightforward one. In particular, our computation reveals some new cohomological classes for the algebra H(2|0) (and also for the Poisson algebra Po(2|0)).

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