Modular vector fields in non-commutative geometry

Toyo Taniguchi

doi:10.1016/j.geomphys.2025.105565

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arXiv · 2410.24064

Modular vector fields in non-commutative geometry

Toyo Taniguchi

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Abstract

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 $\mu$ similar to the one obtained by Alekseev-Kawazumi-Kuno-Naef and the author.

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Toyo Taniguchi. 2024-10-31. Modular vector fields in non-commutative geometry. https://doi.org/10.1016/j.geomphys.2025.105565

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