Letters in Mathematical Physics

, Volume 95, Issue 1, pp 27–39 | Cite as

A Note on the Koszul Complex in Deformation Quantization

  • Andrea Ferrario
  • Carlo Antonio Rossi
  • Thomas Willwacher


The aim of this short note is to present a proof of the existence of an A -quasi-isomorphism between the A -S(V *)-\({\wedge(V)}\) -bimodule K, introduced in Calaque et al. (Bimodules and branes in deformation quantization, 2009), and the Koszul complex K(V) of S(V *), viewed as an A -S(V *)-\({\wedge(V)}\) -bimodule, for V a finite-dimensional (complex or real) vector space.

Mathematics Subject Classification (2000)

16E45 81R60 


Koszul duality A-algebras and -bimodules deformation quantization 


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Copyright information

© Springer 2010

Authors and Affiliations

  • Andrea Ferrario
    • 1
  • Carlo Antonio Rossi
    • 2
  • Thomas Willwacher
    • 1
  1. 1.Department of MathematicsETH ZurichZurichSwitzerland
  2. 2.Departamento de Matemática, Centro de Análise Matemática, Geometria e Sistemas DinâmicosInstituto Superior TécnicoLisboaPortugal

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