标题： 张量积和局部性设置中的Milnor-Moore定理 显示英文标题

标题： Tensor products and the Milnor-Moore theorem in the locality setup

摘要： 本文的探索性论文讨论了局部性框架中的张量积{在先前工作中开发的}，这是量子场论中局部性原理代数表述的自然背景。 局部性向量空间的局部性张量积提出了具有挑战性的问题，例如两个局部性向量空间的局部性张量积是否是一个局部性向量空间。 一个相关问题是商局部性向量空间是否是一个局部性向量空间，我们首先在群论语言中重新解释它，然后用短正合序列来表示。 我们证明了局部性张量代数和局部性包络代数的普遍性质，它们是张量代数和包络代数在局部性框架中的类似物。 这些普遍性质在张量积构造中底层的局部性和多重线性之间的兼容性假设下成立，我们以猜想陈述的形式表述这些假设。 假设这些假设成立，我们将Milnor-Moore定理推广到局部性设置，并讨论其一些后果。 显示英文摘要

摘要： 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.