A proof of the Tsygan formality conjecture for chains
| dc.creator | Shoikhet, Boris | |
| dc.date | 2000-10-31 | |
| dc.date | 2000-12-05 | |
| dc.date.accessioned | 2026-07-07T04:38:22Z | |
| dc.date.available | 2026-07-07T04:38:22Z | |
| dc.description | We extend the Kontsevich formality $L_\infty$-morphism $\U\colon T^\ndot_\poly(\R^d)\to\D^\ndot_\poly(\R^d)$ to an $L_\infty$-morphism of an $L_\infty$-modules over $T^\ndot_\poly(\R^d)$, $\hat \U\colon C_\ndot(A,A)\toΩ^\ndot(\R^d)$, $A=C^\infty(\R^d)$. The construction of the map $\hat \U$ is given in Kontsevich-type integrals. The conjecture that such an $L_\infty$-morphism exists is due to Boris Tsygan \cite{Ts}. As an application, we obtain an explicit formula for isomorphism $A_*/[A_*,A_*]\simto A/\{A,A\}$ ($A_*$ is the Kontsevich deformation quantization of the algebra $A$ by a Poisson bivector field, and $\{{,}\}$ is the Poisson bracket). We also formulate a conjecture extending the Kontsevich theorem on the cup-products to this context. The conjecture implies a generalization of the Duflo formula, and many other things. | |
| dc.description | LaTeX, 24 pages, 5 eps figures | |
| dc.identifier | https://arxiv.org/abs/math/0010321 | |
| dc.identifier | http://arxiv.org/abs/math/0010321 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60255 | |
| dc.subject | Quantum Algebra | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Commutative Algebra | |
| dc.subject | K-Theory and Homology | |
| dc.subject | Primary 53D55, 18G55, 13D03, 19D55, Secondary 57R56, 81T18 | |
| dc.title | A proof of the Tsygan formality conjecture for chains | |
| dc.type | text |