Kontsevich's Cocycle Construction and Quantization of the Loday-Quillen-Tsygan Theorem

Fuente: arXiv
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Main Author: Ulmer, Jakob
Format: Preprint
Published: 2025
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_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