Quantizing Poisson Manifolds

1997/01/16 by Voronov, Alexander A.
#16E40 (Primary) 81S10 #16S80 #55P62 (Secondary) #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.q-alg/9701017

Abstract

This paper extends Kontsevich's ideas on quantizing Poisson manifolds. A new differential is added to the Hodge decomposition of the Hochschild complex, so that it becomes a bicomplex, even more similar to the classical Hodge theory for complex manifolds.

Related

• Kontsevich's deformation quantization: from Dirac to multiple zeta values
• Lectures on Deformation quantization of Poisson manifolds
• Sur la conjecture combinatoire de Kashiwara-Vergne
• A Canonical Quantization of Poisson Manifolds: a 2-Groupoid Scheme
• Semiclassical Hodge theory for log Poisson manifolds