论文标题
当地设置中的张量产品和Milnor-Moore定理
Tensor products and the Milnor-Moore theorem in the locality setup
论文作者
论文摘要
目前的探索性论文涉及量子框架中的张量产品{在先前的工作中开发}，这是量子场理论中局部原理代数制定的自然环境。位置向量空间的局部张量产品提出了具有挑战性的问题，例如两个位置向量空间的局部张量产品是否是局部矢量空间。一个相关的问题是，局部矢量空间的商是否是局部矢量空间，我们首先以组理论语言重新解释了该空间，然后以简短的精确序列进行重新诠释。我们证明了局部张量代数的通用属性和包围代数的局部性，即张量代数的局部框架中的类似物和包络代数。这些通用性质在兼容性假设和张量产品的构建基础性的兼容性假设下，我们以猜想的陈述形式制定。假设它们成立，我们将Milnor-Moore定理推广到当地设置，并讨论其一些后果。
The present exploratory paper deals with tensor products in the locality framework {developed in previous work}, a natural setting for an algebraic formulation of the locality principle in quantum field theory. Locality tensor products of locality vector spaces raise challenging questions, such as whether the locality tensor product of two locality vector spaces is a locality vector space. A related question is whether the quotient of locality vector spaces is a locality vector space, which we first reinterpret in a group theoretic language and then in terms of short exact sequences. We prove a universal property for the locality tensor algebra and for the locality enveloping algebra, the analogs in the locality framework of the tensor algebra and of the enveloping algebra. These universal properties hold under compatibility assumptions between the locality and the multilinearity underlying the construction of tensor products which we formulate in the form of conjectural statements. Assuming they hold true, we generalise the Milnor-Moore theorem to the locality setup and discuss some of its consequences.
