2003/07/03 by Tom Lada, Martin Markl, Lada, Tom +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Black Holes and Theoretical Physics #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.QA
paper · pdf · doi:10.48550/arxiv.math/0307054
19 pages; two new sections added: "Equivalence between symmetric brace algebras and pre-Lie algebras" and "Transfers of strongly homotopy structures"
openalex publication_date 2003/07/03 · arxiv created 2005/03/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop a symmetric analog of brace algebras and discuss the relation of such algebras to L∞-algebras. We give an alternate proof that the category of symmetric brace algebras is isomorphic to the category of pre-Lie algebras. As an application, symmetric braces are used to describe transfers of strongly homotopy structures. We then explain how these symmetric brace algebras may be used to examine the L∞-algebras that result from a particular gauge theory for massless particles of high spin.