论文标题
由链复合物确定的持续谎言代数
Continual Lie algebras determined by chain complexes
论文作者
论文摘要
连续的代数是通过考虑持续的根系来对谎言代数的无限维代数概括。在本文中，我们建立了链复合物与持续谎言代数之间的一般关系。自然正交性条件相对于链条复合物$ \ Mathcal c $ spaces的元素之间的产品，使$ \ Mathcal c $具有具有差异关系的分级代数的结构。我们证明了本文的主要结果：链条复合物赋予其空间元素的适当莱布尼兹 - 陶艺产品 带来了连续的谎言代数的结构，其根空间由复合物的参数确定。这提供了连续谎言代数的新示例的新来源。最后，举例来说，我们考虑了与光滑歧管叶片相关的čech-de rham复合物的情况。在该链复合物的特定情况下，我们明确得出相应的连续谎言代数的换向关系。
Continual Lie algebras are infinite-dimensional generalizations of Lie algebras with discrete root system by considering continual root systems. In this paper we establish a general relation between chain complexes and continual Lie algebras. The natural orthogonality condition with respect to a product among elements of a chain complex $\mathcal C$ spaces brings about to $\mathcal C$ the structure of a graded algebra with differential relations. We prove the main result of this paper: a chain complex endowed with an appropriate Leibniz-property product of elements of its spaces brings about the structure of a continual Lie algebra with the root space determined by parameters for the complex. That provides a new source of examples of continual Lie algebras. Finally, as an example, we consider the case of Čech-de Rham complex associated to a foliation of a smooth manifold. In a particular case of this chain complex, we derive explicitly the commutation relations for the corresponding continual Lie algebra.
