Non-commutative divergence and the Turaev cobracket
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911169802928128 |
|---|---|
| author | Taniguchi, Toyo |
| author_facet | Taniguchi, Toyo |
| contents | The divergence map, an important ingredient in the algebraic description of the Turaev cobracket on a connected oriented compact surface with boundary, is reformulated in the context of non-commutative geometry using a flat connection on the space of 1-forms on a formally smooth associative algebra. We then extend this construction to the case of associative algebras with any finite cohomological dimension, which allows us to give a similar algebraic description of the Turaev cobracket on a closed surface. We also look into a relation between the Satoh trace and the divergence map on a free Lie algebra via geometry over Lie operad. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_16566 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-commutative divergence and the Turaev cobracket Taniguchi, Toyo Algebraic Topology Geometric Topology Quantum Algebra 57K20 (primary) 16D20, 16E05, 16E10, 16S34, 16T05, 58B34 (secondary) The divergence map, an important ingredient in the algebraic description of the Turaev cobracket on a connected oriented compact surface with boundary, is reformulated in the context of non-commutative geometry using a flat connection on the space of 1-forms on a formally smooth associative algebra. We then extend this construction to the case of associative algebras with any finite cohomological dimension, which allows us to give a similar algebraic description of the Turaev cobracket on a closed surface. We also look into a relation between the Satoh trace and the divergence map on a free Lie algebra via geometry over Lie operad. |
| title | Non-commutative divergence and the Turaev cobracket |
| topic | Algebraic Topology Geometric Topology Quantum Algebra 57K20 (primary) 16D20, 16E05, 16E10, 16S34, 16T05, 58B34 (secondary) |
| url | https://arxiv.org/abs/2403.16566 |