Kontsevich's Cocycle Construction and Quantization of the Loday-Quillen-Tsygan Theorem
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913900757254144 |
|---|---|
| author | Ulmer, Jakob |
| author_facet | Ulmer, Jakob |
| contents | We relate graph complexes, Calabi-Yau $A_\infty$-categories and Kontsevich's cocycle construction. Our main result produces a commutative square of shifted Poisson algebras; one of its edges is the Loday-Quillen-Tsygan map, generalized to $A_\infty$-categories. We describe a quantized version via Beilinson-Drinfeld algebras. The larger context is to provide categorical methods which relate enumerative geometry (as in mirror symmetry) and large $N$ gauge theories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_15210 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Kontsevich's Cocycle Construction and Quantization of the Loday-Quillen-Tsygan Theorem Ulmer, Jakob Quantum Algebra Mathematical Physics Algebraic Topology 81T70, 81R60, 53D37, 16E40, 18G85 We relate graph complexes, Calabi-Yau $A_\infty$-categories and Kontsevich's cocycle construction. Our main result produces a commutative square of shifted Poisson algebras; one of its edges is the Loday-Quillen-Tsygan map, generalized to $A_\infty$-categories. We describe a quantized version via Beilinson-Drinfeld algebras. The larger context is to provide categorical methods which relate enumerative geometry (as in mirror symmetry) and large $N$ gauge theories. |
| title | Kontsevich's Cocycle Construction and Quantization of the Loday-Quillen-Tsygan Theorem |
| topic | Quantum Algebra Mathematical Physics Algebraic Topology 81T70, 81R60, 53D37, 16E40, 18G85 |
| url | https://arxiv.org/abs/2506.15210 |