Computation of Cohomology of Lie Algebra of Hamiltonian Vector Fields by Splitting Cochain Complex into Minimal Subcomplexes
Vladimir V. Kornyak
计算同源或同理学本质上是一个高度组合复杂性的问题。 最近,我们提出了一种新的高效算法,用于计算Lie代数和超代数的同源。 该算法基于将整个共链复合物分割成最小的子复合物。 该算法被实现为C程序LieCohomology。 在本文中,我们介绍了将程序LieCohomology应用于汉密尔顿矢量场H(2|0)代数的结果。 我们证明,与直接的方法相比,新方法的效率要高得多。 特别是,我们的计算揭示了代数H(2|0)的一些新的同源类(以及Poisson代数Po(2|0))。
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 th...