Higher order Whitehead products and $L_\infty$ structures on the homology of a DGL

TL;DR

This paper explores the relationship between higher order Whitehead products in the homology of a differential graded Lie algebra and the higher brackets in the transferred $L_ abla$ structure, revealing a new way to understand these algebraic operations.

Contribution

It establishes a connection between Whitehead products and $L_ abla$ structures on homology, providing a novel perspective on their interplay in DGLs.

Findings

Higher Whitehead products are detected via $L_ abla$ brackets.

The transferred $L_ abla$ structure encodes higher order Whitehead products.

The approach offers a new method to analyze homotopy invariants in DGLs.

Abstract

We detect higher order Whitehead products on the homology $H$ of a differential graded Lie algebra $L$ in terms of higher brackets in the transferred $L_\infty$ structure on $H$ via a given homotopy retraction of $L$ onto $H$.