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Trace Functionals on Noncommutative Deformations of Moduli Spaces of Flat Connections

✍ Scribed by Philippe Roche; András Szenes

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
383 KB
Volume
168
Category
Article
ISSN
0001-8708

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✦ Synopsis

We describe an efficient construction of a canonical noncommutative deformation of the algebraic functions on the moduli spaces of flat connections on a Riemann surface. The resulting algebra is a variant of the quantum moduli algebra introduced by Alekseev, Grosse, and Schomerus and Buffenoir and Roche. We construct a natural trace functional on this algebra and show that it is related to the canonical trace in the formal index theory of Fedosov and Nest and Tsygan via Verlinde's formula.

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