向量场李超代数的上同调计算
Computation of Cohomology of Lie Superalgebras of Vector Fields
AI总结：
本文提出一种算法及C语言实现，用于计算李（超）代数上同调，尤其针对形式向量场李超代数，并给出Buttin向量场及相关代数的计算结果，以支持超对称模型研究。
摘要：
李（超）代数的上同调在数学和物理学中有许多重要应用。它承载了所考虑代数的大部分基本（“拓扑”）信息。目前，由于需要进行非常繁琐的代数计算，不同类别的李（超）代数的显式上同调仅在少数情况下已知。因此，计算机代数方法的应用对于这个问题具有重要意义。我们在此描述一种算法及其C语言实现，用于计算李代数和超代数的上同调。该程序可以处理有限维代数和具有有限维齐次分量的无限维分次代数。在最后一类代数中，形式向量场的李代数和李超代数最为重要。我们给出了Buttin向量场李超代数及相关代数上同调计算的一些结果。这些代数是Poisson和Hamiltonian代数的超类似物，已在理论和数学物理的现代超对称模型中找到了许多应用。
英文摘要：
The cohomology of Lie (super)algebras has many important applications in mathematics and physics. It carries most fundamental ("topological") information about algebra under consideration. At present, because of the need for very tedious algebraic computation, the explicitly computed cohomology for different classes of Lie (super)algebras is known only in a few cases. That is why application of computer algebra methods is important for this problem. We describe here an algorithm and its C implementation for computing the cohomology of Lie algebras and superalgebras. The program can proceed finite-dimensional algebras and infinite-dimensional graded algebras with finite-dimensional homogeneous components. Among the last algebras Lie algebras and superalgebras of formal vector fields are most important. We present some results of computation of cohomology for Lie superalgebras of Buttin vector fields and related algebras. These algebras being super-analogs of Poisson and Hamiltonian algebras have found many applications to modern supersymmetric models of theoretical and mathematical physics.
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