Homotopy characters as a homotopy limit

IF 0.8 4区数学 Q2 MATHEMATICS

Homology Homotopy and Applications Pub Date : 2024-09-18 DOI:10.4310/hha.2024.v26.n2.a1

Sergey Arkhipov, Daria Poliakova

引用次数: 0

Abstract

For a Hopf DG‑algebra corresponding to a derived algebraic group, we compute the homotopy limit of the associated cosimplicial system of DG‑algebras given by the classifying space construction. The homotopy limit is taken in the model category of DG‑categories. The objects of the resulting DG‑category are Maurer–Cartan elements of $\operatorname{Cobar}(A)$, or 1‑dimensional $A_\infty$-comodules over $A$. These can be viewed as characters up to homotopy of the corresponding derived group. Their tensor product is interpreted in terms of Kadeishvili’s multibraces. We also study the coderived category of DG‑modules over this DG‑category.

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作为同调极限的同调字符

对于与派生代数群相对应的霍普夫 DG-代数，我们计算分类空间构造给出的相关 DG-代数共简系统的同调极限。同调极限是在 DG 范畴的模型范畴中进行的。由此得到的 DG 范畴的对象是 $\operatorname{Cobar}(A)$ 的毛勒-卡尔坦元素，或者是 $A$ 上的一维 $A_\infty$ 小模子。这些元素可以看作是相应派生类的同调符。它们的张量乘积可以用卡德什维利多臂来解释。我们还研究了这个 DG 范畴上的 DG 模块的编码范畴。

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

Homology Homotopy and Applications 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Homology, Homotopy and Applications is a refereed journal which publishes high-quality papers in the general area of homotopy theory and algebraic topology, as well as applications of the ideas and results in this area. This means applications in the broadest possible sense, i.e. applications to other parts of mathematics such as number theory and algebraic geometry, as well as to areas outside of mathematics, such as computer science, physics, and statistics. Homotopy theory is also intended to be interpreted broadly, including algebraic K-theory, model categories, homotopy theory of varieties, etc. We particularly encourage innovative papers which point the way toward new applications of the subject.