The deformation complex is a homotopy invariant of a homotopy algebra

2013/05/17 by Vasily Dolgushev, Thomas Willwacher, Dolgushev, Vasily +1 · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Quantum Algebra (math.QA) #math.KT #math.QA

paper · pdf · doi:10.48550/arxiv.1305.4165

A revised version. The final version will appear in the volume "Current Developments and Retrospectives in Lie Theory"

openalex publication_date 2013/05/17 · arxiv created 2013/12/16 · arxiv updated 2013/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

To a homotopy algebra one may associate its deformation complex, which is naturally a differential graded Lie algebra. We show that infinity quasi-isomorphic homotopy algebras have L-infinity quasi-isomorphic deformation complexes by an explicit construction.

Cited by

• Simplicial properadic homotopy

Related

• Deformation of L_∞-Algebras
• Derived deformation theory of algebraic structures
• Models for classifying spaces and derived deformation theory
• Deformation theory and Lie algebra homology
• Deformation theory via differential graded Lie algebras