The Hopf Algebraic Structure of Finitely Supported Currents on a Lie Group
Differential Geometry
2026-04-24 v1
Abstract
The space of de Rham currents supported in finitely many points in a Lie group has the structure of a filtered differential graded Hopf algebra. The product is given by convolution of compactly supported currents, and the co-product dualizes to wedge product on differential forms. This space arises as the finitely supported sections functor applied to the bundle of currents on supported at a single (variable) point, and the differential Hopf algebra operations pull back via to bundle maps. Explicit formulas for these bundle maps are obtained, and we show in particular that the convolution product takes the form of a Hopf-algebraic smash product.
Cite
@article{arxiv.2604.21178,
title = {The Hopf Algebraic Structure of Finitely Supported Currents on a Lie Group},
author = {Harrison Pugh},
journal= {arXiv preprint arXiv:2604.21178},
year = {2026}
}