Matches in SemOpenAlex for { <https://semopenalex.org/work/W1644996872> ?p ?o ?g. }
Showing items 1 to 42 of
42
with 100 items per page.
- W1644996872 abstract "Let $alpha$ be a polynomial Poisson bivector on a finite-dimensional vector space $V$ over $mathbb{C}$. Then Kontsevich [K97] gives a formula for a quantization $fstar g$ of the algebra $S(V)^*$. We give a construction of an algebra with the PBW property defined from $alpha$ by generators and relations. Namely, we define an algebra as the quotient of the free tensor algebra $T(V^*)$ by relations $x_iotimes x_j-x_jotimes x_i=R_{ij}(hbar)$ where $R_{ij}(hbar)in T(V^*)otimeshbar mathbb{C}[[hbar]]$, $R_{ij}=hbar Sym(alpha_{ij})+mathcal{O}(hbar^2)$, with one relation for each pair of $i,j=1...dim V$. We prove that the constructed algebra obeys the PBW property, and this is a generalization of the Poincar'{e}-Birkhoff-Witt theorem. In the case of a linear Poisson structure we get the PBW theorem itself, and for a quadratic Poisson structure we get an object closely related to a quantum $R$-matrix on $V$. At the same time we get a free resolution of the deformed algebra (for an arbitrary $alpha$). The construction of this PBW algebra is rather simple, as well as the proof of the PBW property. The major efforts should be undertaken to prove the conjecture that in this way we get an algebra isomorphic to the Kontsevich star-algebra." @default.
- W1644996872 created "2016-06-24" @default.
- W1644996872 creator A5085727267 @default.
- W1644996872 date "2007-06-15" @default.
- W1644996872 modified "2023-09-27" @default.
- W1644996872 title "Koszul duality in deformation quantization, I" @default.
- W1644996872 cites W2491274460 @default.
- W1644996872 hasPublicationYear "2007" @default.
- W1644996872 type Work @default.
- W1644996872 sameAs 1644996872 @default.
- W1644996872 citedByCount "0" @default.
- W1644996872 crossrefType "posted-content" @default.
- W1644996872 hasAuthorship W1644996872A5085727267 @default.
- W1644996872 hasConcept C114614502 @default.
- W1644996872 hasConcept C136119220 @default.
- W1644996872 hasConcept C168619227 @default.
- W1644996872 hasConcept C169171071 @default.
- W1644996872 hasConcept C188845816 @default.
- W1644996872 hasConcept C197375991 @default.
- W1644996872 hasConcept C202444582 @default.
- W1644996872 hasConcept C33923547 @default.
- W1644996872 hasConcept C4161247 @default.
- W1644996872 hasConcept C51255310 @default.
- W1644996872 hasConcept C51568863 @default.
- W1644996872 hasConceptScore W1644996872C114614502 @default.
- W1644996872 hasConceptScore W1644996872C136119220 @default.
- W1644996872 hasConceptScore W1644996872C168619227 @default.
- W1644996872 hasConceptScore W1644996872C169171071 @default.
- W1644996872 hasConceptScore W1644996872C188845816 @default.
- W1644996872 hasConceptScore W1644996872C197375991 @default.
- W1644996872 hasConceptScore W1644996872C202444582 @default.
- W1644996872 hasConceptScore W1644996872C33923547 @default.
- W1644996872 hasConceptScore W1644996872C4161247 @default.
- W1644996872 hasConceptScore W1644996872C51255310 @default.
- W1644996872 hasConceptScore W1644996872C51568863 @default.
- W1644996872 hasLocation W16449968721 @default.
- W1644996872 hasOpenAccess W1644996872 @default.
- W1644996872 hasPrimaryLocation W16449968721 @default.
- W1644996872 isParatext "false" @default.
- W1644996872 isRetracted "false" @default.
- W1644996872 magId "1644996872" @default.
- W1644996872 workType "article" @default.