In earlier work, Helen Wong and the author discovered certain “miraculous cancellations” for the quantum trace map connecting the Kauffman bracket skein algebra of a surface to its quantum Teichmüller space, occurring when the quantum parameter is a root of unity. The current paper is devoted to giving a more representation theoretic interpretation of this phenomenon, in terms of the quantum group and its dual Hopf algebra .
Des travaux précédents de Helen Wong et de l’auteur ont mis en évidence, quand le paramètre quantique est une racine de l’unité, des « annulations miraculeuses » pour l’application de trace quantique qui relie l’algèbre d’écheveaux du crochet de Kauffman à l’espace de Teichmüller quantique d’une surface. L’article ci-dessous fournit une interprétation plus conceptuelle de ce phénomène, en termes de représentations du groupe quantique et de son algèbre de Hopf duale .
@article{AFST_2019_6_28_3_523_0, author = {Bonahon, Francis}, title = {Miraculous cancellations for quantum $\protect \mathrm{SL}_2$}, journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques}, pages = {523--557}, publisher = {Universit\'e Paul Sabatier, Toulouse}, volume = {Ser. 6, 28}, number = {3}, year = {2019}, doi = {10.5802/afst.1608}, language = {en}, url = {http://www.numdam.org/articles/10.5802/afst.1608/} }
TY - JOUR AU - Bonahon, Francis TI - Miraculous cancellations for quantum $\protect \mathrm{SL}_2$ JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2019 SP - 523 EP - 557 VL - 28 IS - 3 PB - Université Paul Sabatier, Toulouse UR - http://www.numdam.org/articles/10.5802/afst.1608/ DO - 10.5802/afst.1608 LA - en ID - AFST_2019_6_28_3_523_0 ER -
%0 Journal Article %A Bonahon, Francis %T Miraculous cancellations for quantum $\protect \mathrm{SL}_2$ %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2019 %P 523-557 %V 28 %N 3 %I Université Paul Sabatier, Toulouse %U http://www.numdam.org/articles/10.5802/afst.1608/ %R 10.5802/afst.1608 %G en %F AFST_2019_6_28_3_523_0
Bonahon, Francis. Miraculous cancellations for quantum $\protect \mathrm{SL}_2$. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume spécial en l’honneur de Jean-Pierre OTAL “Low dimensional topology, hyperbolic manifolds and spectral geometry”, Volume 28 (2019) no. 3, pp. 523-557. doi : 10.5802/afst.1608. http://www.numdam.org/articles/10.5802/afst.1608/
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