Extensions between functors from Jacobi diagrams in handlebodies

2025/09/23 by Katada, Mai
#18A25 #18A40 #18G15 #57K16 #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2510.09625

Abstract

The first Ext-groups between Schur functors in the category of modules over the \Bbbk-linearization \Bbbkgr^op of the opposite of the category of finitely generated free groups are computed for a filed \Bbbk of characteristic 0. The \Bbbk-linear category A of Jacobi diagrams in handlebodies, which was introduced by Habiro and Massuyeau, has an ℕ-grading whose degree 0 part identifies with the category \Bbbkgr^op. We compute the first Ext-groups in the category of A-modules between simple A-modules which are induced by Schur functors.

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Related

• On the functors associated with beaded open Jacobi diagrams
• Modules over the category of Jacobi diagrams in handlebodies
• On the Passi and the Mal'cev functors
• Actions of automorphism groups of free groups on spaces of Jacobi diagrams. I
• Comparing Translation and Jaquet functor over general linear groups