On the homotopy of simplicial algebras over an operad

Author:

Fresse Benoit

Abstract

According to a result of H. Cartan, the homotopy of a simplicial commutative algebra is equipped with divided power operations. In this article, we show how to extend this result to other kinds of algebras. For instance, we prove that the homotopy of a simplicial Lie algebra is equipped with the structure of a restricted Lie algebra.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference30 articles.

1. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences];Barr, Michael,1985

2. A.K. Bousfield, Homogeneous functors and their derived functors, Unpublished manuscript, Brandeis University (1967).

3. \bysame, Operations on derived functors of non-additive functors, Unpublished manuscript, Brandeis University (1967).

4. The 𝑚𝑜𝑑-𝑝 lower central series and the Adams spectral sequence;Bousfield, A. K.;Topology,1966

5. H. Cartan, Algèbres d’Eilenberg-MacLane et homotopie, Séminaire Henri Cartan, 1954-55.

Cited by 26 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Divided power algebras and distributive laws;Journal of Pure and Applied Algebra;2023-08

2. Derived homotopy algebras;Proceedings of the Royal Society of Edinburgh: Section A Mathematics;2022-07-25

3. Resolutions of operads via Koszul (bi)algebras;Journal of Homotopy and Related Structures;2022-03-03

4. ℰn–Hopf invariants;Algebraic & Geometric Topology;2020-12-08

5. Plethysm and cohomology representations of external and symmetric products;Advances in Mathematics;2020-12

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3