Resumen de Linear Batalin–Vilkovisky quantization as a functor of ∞-categories

Owen Gwilliam, Rune Haugseng

• We study linear Batalin–Vilkovisky (BV) quantization, which is a derived and shifted version of the Weyl quantization of symplectic vector spaces. Using a variety of homotopical machinery, we implement this construction as a symmetric monoidal functor of ∞ -categories. We also show that this construction has a number of pleasant properties: It has a natural extension to derived algebraic geometry, it can be fed into the higher Morita category of En -algebras to produce a “higher BV quantization” functor, and when restricted to formal moduli problems, it behaves like a determinant. Along the way we also use our machinery to give an algebraic construction of En -enveloping algebras for shifted Lie algebras.