Deformation quantization of gerbes

By P. Bressler, A. Gorokhovsky, R. Nest, B. Tsygan. 2005

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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.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5f910762888ae37714bdedb5e43675feb6cb78bc