Paper Info
Title
A Method of Splitting Cochain Complexes for Computing Cohomology: Lie Algebra of Hamiltonian Vector Fields H(2|0)
Abstract
Computation of homology or cohomology is inherently a problem of high combinatorial complexity. Recently, we have proposed a new algorithm for computing cohomology of Lie (super)algebras. This algorithm is based on splitting a complete cochain complex into minimal subcomplexes. The algorithm is implemented in C as a program LieCohomology. This paper presents results of computation of cohomology in a trivial module for a Lie algebra of Hamiltonian vector fields H(2|0). We demonstrate that the new approach is much more efficient than the traditional one. In particular, we have revealed some new cohomology classes for the H(2|0) algebra and the related Lie algebra of the Poisson vector fields Po(2|0).
Year
DOI
Venue
2003
10.1023/A:1022900816799
Programming and Computer Software
Keywords
Field
DocType
minimal subcomplexes,new cohomology class,lie algebra,hamiltonian vector fields h,new algorithm,new approach,complete cochain complex,high combinatorial complexity,splitting cochain complexes,poisson vector field,computing cohomology,related lie algebra,vector field
Discrete mathematics,De Rham cohomology,Graded Lie algebra,Algebra,Lie coalgebra,Universal enveloping algebra,Equivariant cohomology,Lie conformal algebra,Cohomology,Mathematics,Group cohomology
Journal
Volume
Issue
ISSN
29
2
1608-3261
Citations 
PageRank 
References 
1
0.48
2
Authors
1
Name
Order
Citations
PageRank
V. V. Kornyak11212.76