2024/10/31 by Taniguchi, Toyo · 1 citation
#16S34 #55P50 #57K20 (primary) 16D20 #58B34 (secondary) #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.2410.24064
We construct a non-commutative analogue of the modular vector field on a Poisson manifold for a given pair of a double bracket and a connection on a space of 1-forms. The key ingredient, the triple divergence map, is directly constructed from a connection on a linear category to deal with multiple base points. As an application, we give an algebraic description of the framed, groupoid version of Turaev's loop operation μ similar to the one obtained by Alekseev-Kawazumi-Kuno-Naef and the author.