Deformation quantization of gerbes

Paul Bressler, Alexander Gorokhovsky, Ryszard Nest, Boris Tsygan*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

29 Scopus citations

Abstract

This is the first in a series of articles devoted to deformation quantization of gerbes. We introduce basic definitions, interpret deformations of a given stack as Maurer-Cartan elements of a differential graded Lie algebra (DGLA), and classify deformations of a given gerbe in terms of Maurer-Cartan elements of the DGLA of Hochschild cochains twisted by the cohomology class of the gerbe. We also classify all deformations of a given gerbe on a symplectic manifold, as well as provide a deformation-theoretic interpretation of the first Rozansky-Witten class.

Original languageEnglish (US)
Pages (from-to)230-266
Number of pages37
JournalAdvances in Mathematics
Volume214
Issue number1
DOIs
StatePublished - Sep 10 2007

Keywords

  • Deformation
  • Quantization

ASJC Scopus subject areas

  • Mathematics(all)

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