Carlo A. Rossi
A note on the Koszul complex in deformation quantization.
Mon, 02/15/2010 - 16:01 — SomNambulAuthors: Andrea Ferrario, Carlo A. Rossi, Thomas Willwacher
Subjects: Quantum Algebra
AbstractThe aim of this short note is to present a proof of Conjecture 1.3 of
\cite{CFFR} about the existence of an $A_\infty$-quasi-isomorphism between the
$A_\infty$-$\mathrm S(V^*)$-$\wedge(V)$-bimodule $K$, introduced in
\cite{CFFR}, and the Koszul complex $\mathrm K(V)$ of $\mathrm S(V^*)$, viewed
as a $\mathrm S(V^*)$-$\wedge(V)$-bimodule, for $V$ a finite-dimensional
(complex or real) vector space.Deformation quantization with generators and relations.
Tue, 11/24/2009 - 16:01 — SomNambulAuthors: Damien Calaque, Giovanni Felder, Carlo A. Rossi
Subjects: Quantum Algebra
AbstractIn this paper we prove a conjecture of B. Shoikhet which claims that two
quantization procedures arising from Fourier dual constructions actually
coincide.Hochschild cohomology for Lie algebroids.
Thu, 08/20/2009 - 23:06 — SomNambulAuthors: Damien Calaque, Carlo A. Rossi, Michel Van den Bergh
Subjects: Algebraic Geometry
AbstractWe define the Hochschild (co)homology of a ringed space relative to a locally
free Lie algebroid. Our definitions mimic those of Swan and Caldararu for an
algebraic variety. We show that our (co)homology groups can be computed using
suitable standard complexes.Our formulae depend on certain natural structures on jetbundles over Lie
algebroids. In an appendix we explain this by showing that such jetbundles are
formal groupoids which serve as the formal exponentiation of the Lie algebroid.Bimodules and branes in deformation quantization.
Tue, 08/18/2009 - 11:53 — SomNambulAuthors: Damien Calaque, Giovanni Felder, Andrea Ferrario, Carlo A. Rossi
Subjects: Quantum Algebra
AbstractWe prove a version of Kontsevich's formality theorem for two subspaces
(branes) of a vector space $X$. The result implies in particular that the
Kontsevich deformation quantizations of $\mathrm{S}(X^*)$ and $\wedge(X)$
associated with a quadratic Poisson structure are Koszul dual. This answers an
open question in Shoikhet's recent paper on Koszul duality in deformation
quantization.- 13 comments
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