Coherent quantization using coloured surfaces

In this note, we revisit the quantization of Lie bialgebras described by the second author in [28], placing it in the more general framework of quantizing moduli spaces developed in [29]. In particular, we show that embeddings of quilted surfaces (which are compatible with the choice of skeleton) induce morphisms between the corresponding quantized moduli spaces of flat connections. As an application, we describe quantizations of both the variety of Lagrangian subalgebras and the de-Cocini Procesi wonderful compactification, which are compatible with the action of the (quantized) Poisson Lie group.

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P. Ševera was supported by the grant MODFLAT of the European Research Council, and by NCCR SwissMAP of the Swiss National Science Foundation.

Received 1 February 2016

Accepted 29 August 2018

Published 25 October 2019