2025/07/22 by Zsuzsanna Dancso, Iva Halacheva, Dancso, Zsuzsanna +7 · 1 citation
Computer Science · Mathematics · #17B #18M60 #55 #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Category Theory (math.CT) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.2507.16243
openalex publication_date 2025/07/22 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28
Using the language of moperads -- monoids in the category of right modules over an operad -- we reinterpret the Alekseev--Enriquez--Torossian construction of Kashiwara--Vergne (KV) solutions from associators. We show that any equivalence between the moperad of parenthesized braids with a frozen strand and the moperad of chord diagrams gives rise to a family of genus zero KV solutions operadically generated by a single classical KV solution. We show that the Grothendieck--Teichmüller module groups act on the latter, intertwining the actions of the KV symmetry groups. In the other direction, we show that any symmetric KV solution gives rise to a module map from parenthesized braids with a frozen strand to tangential automorphisms of free Lie algebras. This map factors through the moperad of chord diagrams if and only if the associated KV associator is a Drinfeld associator.