哈密顿向量场李代数上同调的计算：将上链复形分解为最小子复形
Computation of Cohomology of Lie Algebra of Hamiltonian Vector Fields by Splitting Cochain Complex into Minimal Subcomplexes
AI总结：
本文提出一种基于将上链复形分解为最小子复形的高效算法，并应用于哈密顿向量场代数H(2|0)的上同调计算，显著提升效率并发现新的上同调类。
摘要：
同调或上同调的计算本质上是一个具有高组合复杂度的问题。最近，我们提出了一种新的高效算法，用于计算李代数和超李代数的上同调。该算法基于将完整的上链复形划分为最小子复形。该算法已作为C程序LieCohomology实现。在本文中，我们展示了将程序LieCohomology应用于哈密顿向量场代数H(2|0)的结果。我们证明了新方法比直接方法高效得多。特别是，我们的计算揭示了代数H(2|0)（以及泊松代数Po(2|0)）的一些新的上同调类。
英文摘要：
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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