Categorification of the virtual braid groups
Annales mathématiques Blaise Pascal, Volume 18 (2011) no. 2, pp. 231-243.

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

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

DOI: 10.5802/ambp.297
Classification: 20F36,  05E10,  05E18,  13D99,  18G35
Keywords: braid group, virtual braid, categorification
Anne-Laure Thiel 1

1 Institut de Recherche Mathématique Avancée, Université de Strasbourg et CNRS 7 rue René Descartes, F–67084 Strasbourg Cedex, France
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Anne-Laure Thiel. Categorification of the virtual braid groups. Annales mathématiques Blaise Pascal, Volume 18 (2011) no. 2, pp. 231-243. doi : 10.5802/ambp.297. https://ambp.centre-mersenne.org/articles/10.5802/ambp.297/

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

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

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

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

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

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

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

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

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

[13] V. V. Vershinin 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

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