2006/06/14 by Muriel Livernet, Livernet, Muriel, Frédéric Patras +2
Mathematics · #18D50: 16W30: 17A30: 17B63 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #math.QA #math.RA #msc:17B63
paper · pdf · doi:10.48550/arxiv.math/0606329
23 pages. Using xyPic
arxiv created 2006/06/14 · openalex publication_date 2006/06/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The present article takes advantage of the properties of algebras in the category of S-modules (twisted algebras) to investigate further the fine algebraic structure of Hopf operads. We prove that any Hopf operad P carries naturally the structure of twisted Hopf P-algebra. Many properties of classical Hopf algebraic structures are then shown to be encapsulated in the twisted Hopf algebraic structure of the corresponding Hopf operad. In particular, various classical theorems of Lie theory relating Lie polynomials to words (i.e. elements of the tensor algebra) are lifted to arbitrary Hopf operads.