局部性框架下的张量积与Milnor-Moore定理
Tensor products and the Milnor-Moore theorem in the locality setup
摘要：
本探索性的文件涉及张量积的局部性框架{在以前的工作中开发}，自然设置的代数制定的局部性原则在量子场论。局部性向量空间的局部性张量积提出了一个具有挑战性的问题，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。一个相关的问题是局部向量空间的商是否是局部向量空间，我们首先用群论语言重新解释，然后用短正合序列重新解释。本文证明了局部张量代数和局部包络代数的一个泛性质，它们是张量代数和包络代数局部框架中的类似物.这些泛性质的地方和多重线性之间的兼容性假设下，我们制定的形式的结构陈述的张量积的建设。假设他们持有真实的，我们概括的米尔诺尔-摩尔定理的局部设置，并讨论其后果。
英文摘要：
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.
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