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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.21178 |
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| _version_ | 1866910159064793088 |
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| author | Pugh, Harrison |
| author_facet | Pugh, Harrison |
| contents | The space of de Rham currents supported in finitely many points in a Lie group $G$ 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 $ Γ^{finite} $ applied to the bundle $ \mathcal{U}(G) $ of currents on $ G $ supported at a single (variable) point, and the differential Hopf algebra operations pull back via $ Γ^{finite} $ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_21178 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Hopf Algebraic Structure of Finitely Supported Currents on a Lie Group Pugh, Harrison Differential Geometry The space of de Rham currents supported in finitely many points in a Lie group $G$ 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 $ Γ^{finite} $ applied to the bundle $ \mathcal{U}(G) $ of currents on $ G $ supported at a single (variable) point, and the differential Hopf algebra operations pull back via $ Γ^{finite} $ 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. |
| title | The Hopf Algebraic Structure of Finitely Supported Currents on a Lie Group |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2604.21178 |