论文标题
与低维谎言代数相关的超级同源性
Super homologies associated with low dimensional Lie algebras
论文作者
论文摘要
歧管上的泊松结构的特征是Schouten支架。与Schouten支架的切线束的分级代数是Lie Superalgebra的原型。泊松条件意味着在2链空间中的一个周期。鉴于分级的谎言超级级，0级的子空间是谎言代数。在本说明中，使用Schouten支架的切线束的DGA作为模型，我们从抽象的Lie代数开始，由Schouten样支架构造非平凡的Lie Superalgebra。然后自然要问核心谎言如何控制谎言级别的级别。这里的一项试验是研究超级同源组的贝蒂数字。对于阿贝利安（Abelian Lie）代数，边界操作员是微不足道的，因此我们研究了小于4的尺寸的低维非尺寸谎言代数的超同源组。
A Poisson structure on a manifold is characterized by the Schouten bracket. The graded algebra of the tangent bundle with the Schouten bracket is a prototype of Lie superalgebra. The Poisson condition means that a cycle in the 2-chain space. Given a graded Lie superalgebra, the 0-graded subspace is a Lie algebra. In this note, using the DGA of tangent bundle with the Schouten bracket as a model, we start from an abstract Lie algebra, construct non-trivial Lie superalgebra by Schouten-like bracket. Then it is natural to ask how the core Lie algebra control the Lie superalgebra. One trial here is to investigate the Betti numbers of the super homology groups. For abelian Lie algebras, the boundary operator is trivial, so we study super homology groups for low dimensional non-abelian Lie algebras of dimension smaller than 4.
