Deformation quantization of gerbes

• Autores: Paul Bressler, Alexander Gorokhovsky, Ryszard Nest, Boris Tsygan
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 214, Nº 1, 2007, págs. 230-266
• Idioma: inglés
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• Resumen

  • 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.