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Article Dans Une Revue Commun.Math.Phys. Année : 2019

Projective representations of mapping class groups in combinatorial quantization

Résumé

Let $\Sigma _{g,n}$ be a compact oriented surface of genus g with n open disks removed. The algebra $\mathcal {L}_{g,n}(H)$ was introduced by Alekseev–Grosse–Schomerus and Buffenoir–Roche and is a combinatorial quantization of the moduli space of flat connections on $\Sigma _{g,n}$. We construct a projective representation of the mapping class group of $\Sigma _{g,n}$ using $\mathcal {L}_{g,n}(H)$ and its subalgebra of invariant elements. Here we assume that the gauge Hopf algebra H is finite-dimensional, factorizable and ribbon, but not necessarily semi-simple. We also give explicit formulas for the representation of the Dehn twists generating the mapping class group; in particular, we show that it is equivalent to a representation constructed by V. Lyubashenko using categorical methods.

Dates et versions

hal-01960367 , version 1 (19-12-2018)

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Citer

Matthieu Faitg. Projective representations of mapping class groups in combinatorial quantization. Commun.Math.Phys., 2019, 377 (1), pp.161-198. ⟨10.1007/s00220-019-03470-z⟩. ⟨hal-01960367⟩
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