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

• Owen Gwilliam ^[1] ; Rune Haugseng ^[2]
  1. [1] Max Planck Institute for Mathematics

     Max Planck Institute for Mathematics

     Kreisfreie Stadt Bonn, Alemania

     
  2. [2] University of Copenhagen

     University of Copenhagen

     Dinamarca

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 24, Nº. 2, 2018, págs. 1247-1313
• Idioma: inglés
• DOI: 10.1007/s00029-018-0396-0
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• Resumen

  • 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.