no. 2
Categorification of the virtual braid groups
[Catégorification des groupes de tresses virtuelles]
Thiel, Anne-Laure1
1 Institut de Recherche Mathématique Avancée, Université de Strasbourg et CNRS 7 rue René Descartes, F–67084 Strasbourg Cedex, France
Annales mathématiques Blaise Pascal, Tome 18 (2011) no. 2, pp. 231-243.

Nous généralisons la catégorification des groupes de tresses par complexes de bimodules de Soergel due à Rouquier aux groupes de tresses virtuelles.

We extend Rouquier’s categorification of the braid groups by complexes of Soergel bimodules to the virtual braid groups.

DOI : 10.5802/ambp.297
Classification : 20F36, 05E10, 05E18, 13D99, 18G35
Keywords: braid group, virtual braid, categorification
Mot clés : groupe de tresses, tresse virtuelle, catégorification
Thiel, Anne-Laure 1

1 Institut de Recherche Mathématique Avancée, Université de Strasbourg et CNRS 7 rue René Descartes, F–67084 Strasbourg Cedex, France 
@article{AMBP_2011__18_2_231_0,
     author = {Thiel, Anne-Laure},
     title = {Categorification of the virtual braid groups},
     journal = {Annales math\'ematiques Blaise Pascal},
     pages = {231--243},
     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {18},
     number = {2},
     year = {2011},
     doi = {10.5802/ambp.297},
     zbl = {1260.20059},
     mrnumber = {2896487},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/ambp.297/}
}
TY  - JOUR
AU  - Thiel, Anne-Laure
TI  - Categorification of the virtual braid groups
JO  - Annales mathématiques Blaise Pascal
PY  - 2011
SP  - 231
EP  - 243
VL  - 18
IS  - 2
PB  - Annales mathématiques Blaise Pascal
UR  - http://www.numdam.org/articles/10.5802/ambp.297/
DO  - 10.5802/ambp.297
LA  - en
ID  - AMBP_2011__18_2_231_0
ER  - 
%0 Journal Article
%A Thiel, Anne-Laure
%T Categorification of the virtual braid groups
%J Annales mathématiques Blaise Pascal
%D 2011
%P 231-243
%V 18
%N 2
%I Annales mathématiques Blaise Pascal
%U http://www.numdam.org/articles/10.5802/ambp.297/
%R 10.5802/ambp.297
%G en
%F AMBP_2011__18_2_231_0
Thiel, Anne-Laure. Categorification of the virtual braid groups. Annales mathématiques Blaise Pascal, Tome 18 (2011) no. 2, pp. 231-243. doi : 10.5802/ambp.297. http://www.numdam.org/articles/10.5802/ambp.297/

[1] Fenn, R.; Rimányi, R.; Rourke, C. The braid-permutation group, Topology, Volume 36 (1997) no. 1, pp. 123-135 | DOI | MR | Zbl

[2] Kamada, N.; Kamada, S. Abstract link diagrams and virtual knots, J. Knot Theory Ramifications, Volume 9 (2000) no. 1, pp. 93-106 | DOI | MR | Zbl

[3] Kamada, S. Braid presentation of virtual knots and welded knots, Osaka J. Math., Volume 44 (2007) no. 2, pp. 441-458 http://projecteuclid.org/getRecord?id=euclid.ojm/1183667989 | MR | Zbl

[4] Kassel, C.; Turaev, V. Braid groups, Graduate Texts in Mathematics, 247, Springer, New York, 2008 | MR | Zbl

[5] Kauffman, L. H. Virtual knot theory, European J. Combin., Volume 20 (1999) no. 7, pp. 663-690 | DOI | MR | Zbl

[6] Khovanov, M. Triply-graded link homology and Hochschild homology of Soergel bimodules, Internat. J. Math., Volume 18 (2007) no. 8, pp. 869-885 | DOI | MR | Zbl

[7] Kuperberg, G. What is a virtual link?, Algebr. Geom. Topol., Volume 3 (2003), p. 587-591 (electronic) | DOI | MR | Zbl

[8] Manturov, V. O. Knot theory, Chapman & Hall/CRC, Boca Raton, FL, 2004 | MR | Zbl

[9] Mazorchuk, V.; Stroppel, C. On functors associated to a simple root, J. Algebra, Volume 314 (2007) no. 1, pp. 97-128 | DOI | MR | Zbl

[10] Rouquier, R. Categorification of 𝔰𝔩 2 and braid groups, Trends in representation theory of algebras and related topics (Contemp. Math.), Volume 406, Amer. Math. Soc., Providence, RI, 2006, pp. 137-167 | MR | Zbl

[11] Soergel, W. The combinatorics of Harish-Chandra bimodules, J. Reine Angew. Math., Volume 429 (1992), pp. 49-74 | DOI | MR | Zbl

[12] Soergel, W. Gradings on representation categories, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994), Birkhäuser, Basel (1995), pp. 800-806 | MR | Zbl

[13] Vershinin, V. V. On homology of virtual braids and Burau representation, J. Knot Theory Ramifications, Volume 10 (2001) no. 5, pp. 795-812 Knots in Hellas ’98, Vol. 3 (Delphi) | DOI | MR | Zbl

Cité par Sources :