nLab BD operad

Idea

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

See at relation between BV and BD.

Definition

The underlying graded vector spaces are

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

and the differential is

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

(…)

Related concepts

algebraic deformation quantization

dimension	classical field theory	Lagrangian BV quantum field theory	factorization algebra of observables
general $n$	P-n algebra	BD-n algebra?	E-n algebra
$n = 0$	Poisson 0-algebra	BD-0 algebra? = BD algebra	E-0 algebra? = pointed space
$n = 1$	P-1 algebra = Poisson algebra	BD-1 algebra?	E-1 algebra? = A-∞ algebra

References

The BD operad was introduced in

• Alexander Beilinson, Vladimir Drinfeld, Chiral Algebras

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 : $P_0$-operad (wikilass=‘newWikiWord’>P_0%20operad?</span>), pdf)