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Trace functionals on non-commutative deformations of moduli spaces of flat connections

Philippe Roche·Andras Szenes
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Abstract

We describe an efficient construction of a canonical non-commutative deformation of the algebraic functions on the moduli spaces of flat connections on a Riemann surface. We show that this algebra, which is a variant of the quantum moduli algebra introduced by Alekseev-Grosse-Schomerus and Buffenoir-Roche, has a trace functional which is related to the canonical trace in the formal index theory of Fedosov and Nest-Tsygan via the Verlinde formula.

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Philippe Roche, Andras Szenes. 2000-08-18. Trace functionals on non-commutative deformations of moduli spaces of flat connections. https://arxiv.org/abs/math/0008149

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