Vertex algebras and $2$-monoidal categories

IF 0.6 3区 数学 Q3 MATHEMATICS
Estanislao Herscovich
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引用次数: 0

Abstract

In this article we address Problem 5.12 in $\href{https://projecteuclid.org/ebook/Download?urlId=10.2969/aspm/03110051&isFullBook=false}{[9]}$. More precisely, we prove that the singular tensor product introduced by R. Borcherds in the previous reference is part of a 2-monoidal category structure in a certain category of functors. We also complete some missing points in the previously mentioned article, most notably in the definitions of singular tensor products and of vertex algebras themselves, which are however verified in all the examples appearing in that reference. To prove our results it will be extremely useful, if not essential, to frame our objects within the language of bicategories. We also introduce a slightly more general notion of (quantum) vertex algebra than the one in $\href{https://projecteuclid.org/ebook/Download?urlId=10.2969/aspm/03110051&isFullBook=false}{[9]}$, that we call categorical (quantum) vertex algebra, enjoying all the properties mentioned by Borcherds in that article and having as particular example the definition presented by that author.
顶点代数和 2 美元单元范畴
本文将讨论 $\href{https://projecteuclid.org/ebook/Download?urlId=10.2969/aspm/03110051&isFullBook=false}{[9]}$ 中的问题 5.12。更确切地说,我们证明了 R. Borcherds 在前一篇参考文献中引入的奇异张量积是某个函子范畴中的 2 单调范畴结构的一部分。我们还完成了前面提到的文章中的一些缺失点,尤其是奇异张量积和顶点代数本身的定义,不过这些定义在该参考文献中出现的所有例子中都得到了验证。为了证明我们的结果,将我们的研究对象置于二范畴的语言中将是非常有用的,甚至是必不可少的。我们还引入了一个比$\href{https://projecteuclid.org/ebook/Download?urlId=10.2969/aspm/03110051&isFullBook=false}{[9]}$中的(量子)顶点代数稍微更一般的概念,我们称之为分类(量子)顶点代数,它享有鲍彻尔斯在那篇文章中提到的所有性质,并以该作者提出的定义为例。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
1.40
自引率
0.00%
发文量
9
审稿时长
6.0 months
期刊介绍: Dedicated to publication of complete and important papers of original research in all areas of mathematics. Expository papers and research announcements of exceptional interest are also occasionally published. High standards are applied in evaluating submissions; the entire editorial board must approve the acceptance of any paper.
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