Homotopy operations on higher Lie algebras

We determine the multiplicative structures of the homotopy operations on derived Lie algebras, derived restricted Lie algebras and partition Lie algebras, as well as the relation between these. Under Koszul duality, this follows from a calculation of the homotopy operations on derived rings, p-truncated algebras and divided power algebras over $\mathbb{F}_p$.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-27
DOI
https://doi.org/10.48550/arxiv.2610.36942
Primary Topic
Homotopy and Cohomology in Algebraic Topology
Type
preprint
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preprint

Homotopy operations on higher Lie algebras

Joost Nuiten, Jiaqi Fu
arXiv (Cornell University)
Homotopy and Cohomology in Algebraic Topology
preprint

Homotopy operations on higher Lie algebras

Joost Nuiten, Jiaqi Fu
preprint en

Abstract

We determine the multiplicative structures of the homotopy operations on derived Lie algebras, derived restricted Lie algebras and partition Lie algebras, as well as the relation between these. Under Koszul duality, this follows from a calculation of the homotopy operations on derived rings, p-truncated algebras and divided power algebras over $\mathbb{F}_p$.

arXiv (Cornell University)
Homotopy and Cohomology in Algebraic Topology
DOIOpen Access PDFOpenAlex
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Homotopy operations on higher Lie algebras — Joost Nuiten, Jiaqi Fu · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS