Computation of Cohomology of Lie Algebra of Hamiltonian Vector Fields by Splitting Cochain Complex into Minimal Subcomplexes
Abstract
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(20). 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(20) (and also for the Poisson algebra Po(20)).
 Publication:

arXiv Mathematics eprints
 Pub Date:
 May 2002
 DOI:
 10.48550/arXiv.math/0205046
 arXiv:
 arXiv:math/0205046
 Bibcode:
 2002math......5046K
 Keywords:

 Mathematics  Numerical Analysis;
 Mathematical Physics;
 Mathematics  Mathematical Physics;
 Mathematics  Representation Theory
 EPrint:
 8 pages, submitted to CASC2002