nLab BD operad



The Beilinson-Drinfeld operad is the operad whose algebras over an operad are BD algebras.

See at relation between BV and BD.


The underlying graded vector spaces are

BDP 0[[]] BD \coloneqq P_0 \otimes \mathbb{R}[ [\hbar] ]

and the differential is

d(()())={,}. d ( (-)\cdots (-)) = \hbar \{-,-\} \,.


algebraic deformation quantization

dimensionclassical field theoryLagrangian BV quantum field theoryfactorization algebra of observables
general nnP-n algebraBD-n algebra?E-n algebra
n=0n = 0Poisson 0-algebraBD-0 algebra? = BD algebraE-0 algebra? = pointed space
n=1n = 1P-1 algebra = Poisson algebraBD-1 algebra?E-1 algebra? = A-∞ algebra


The BD operad was introduced in

A review in the context of factorization algebras of observables is in section 2.4 of

  • Kevin Costello, Owen Gwilliam, Factorization algebras in perturbative quantum field theory : P 0P_0-operad (wikilass=‘newWikiWord’>P_0%20operad?</span>), pdf)

Last revised on December 21, 2016 at 21:15:49. See the history of this page for a list of all contributions to it.