# The mutation compatibility of the ${\rm SL}_3$ quantum trace maps for surfaces

@inproceedings{Kim2021TheMC, title={The mutation compatibility of the \$\{\rm SL\}\_3\$ quantum trace maps for surfaces}, author={Hyun Kyu Kim}, year={2021} }

Fock-Goncharov’s moduli spaces XPGL3,S of framed PGL3-local systems on punctured surfaces S provide prominent examples of cluster X -varieties and higher Teichmüller spaces. In a previous paper of the author (arXiv:2011.14765), the so-called SL3 quantum trace map is constructed for each triangulable punctured surface S and its ideal triangulation ∆, as a homomorphism from the stated SL3-skein algebra of the surface to a quantum torus algebra that deforms the ring of Laurent polynomials in the…

## One Citation

Quantum traces for $\mathrm{SL}_n(\mathbb{C})$: the case $n=3$.

- Mathematics
- 2021

We generalize Bonahon and Wong's $\mathrm{SL}_2(\mathbb{C})$-quantum trace map to the setting of $\mathrm{SL}_3(\mathbb{C})$. More precisely, for each non-zero complex number $q$, we associate to…

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