Categorification of the virtual braid groups

Anne-Laure Thiel[1]

  • [1] Institut de Recherche Mathématique Avancée, Université de Strasbourg et CNRS 7 rue René Descartes, F–67084 Strasbourg Cedex, France

Annales mathématiques Blaise Pascal (2011)

  • Volume: 18, Issue: 2, page 231-243
  • ISSN: 1259-1734

Abstract

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

How to cite

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Thiel, Anne-Laure. "Categorification of the virtual braid groups." Annales mathématiques Blaise Pascal 18.2 (2011): 231-243. <http://eudml.org/doc/219818>.

@article{Thiel2011,
abstract = {We extend Rouquier’s categorification of the braid groups by complexes of Soergel bimodules to the virtual braid groups.},
affiliation = {Institut de Recherche Mathématique Avancée, Université de Strasbourg et CNRS 7 rue René Descartes, F–67084 Strasbourg Cedex, France},
author = {Thiel, Anne-Laure},
journal = {Annales mathématiques Blaise Pascal},
keywords = {braid group; virtual braid; categorification; generalized braid groups; virtual braid groups; categorifications; cochain complexes},
language = {eng},
month = {7},
number = {2},
pages = {231-243},
publisher = {Annales mathématiques Blaise Pascal},
title = {Categorification of the virtual braid groups},
url = {http://eudml.org/doc/219818},
volume = {18},
year = {2011},
}

TY - JOUR
AU - Thiel, Anne-Laure
TI - Categorification of the virtual braid groups
JO - Annales mathématiques Blaise Pascal
DA - 2011/7//
PB - Annales mathématiques Blaise Pascal
VL - 18
IS - 2
SP - 231
EP - 243
AB - We extend Rouquier’s categorification of the braid groups by complexes of Soergel bimodules to the virtual braid groups.
LA - eng
KW - braid group; virtual braid; categorification; generalized braid groups; virtual braid groups; categorifications; cochain complexes
UR - http://eudml.org/doc/219818
ER -

References

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  1. R. Fenn, R. Rimányi, C. Rourke, The braid-permutation group, Topology 36 (1997), 123-135 Zbl0861.57010MR1410467
  2. N. Kamada, S. Kamada, Abstract link diagrams and virtual knots, J. Knot Theory Ramifications 9 (2000), 93-106 Zbl0997.57018MR1749502
  3. S. Kamada, Braid presentation of virtual knots and welded knots, Osaka J. Math. 44 (2007), 441-458 Zbl1147.57008MR2351010
  4. C. Kassel, V. Turaev, Braid groups, 247 (2008), Springer, New York Zbl1208.20041MR2435235
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  7. G. Kuperberg, What is a virtual link?, Algebr. Geom. Topol. 3 (2003), 587-591 (electronic) Zbl1031.57010MR1997331
  8. V. O. Manturov, Knot theory, (2004), Chapman & Hall/CRC, Boca Raton, FL Zbl1052.57001MR2068425
  9. V. Mazorchuk, C. Stroppel, On functors associated to a simple root, J. Algebra 314 (2007), 97-128 Zbl1152.17002MR2331754
  10. R. Rouquier, Categorification of 𝔰𝔩 2 and braid groups, Trends in representation theory of algebras and related topics 406 (2006), 137-167, Amer. Math. Soc., Providence, RI Zbl1162.20301MR2258045
  11. W. Soergel, The combinatorics of Harish-Chandra bimodules, J. Reine Angew. Math. 429 (1992), 49-74 Zbl0745.22014MR1173115
  12. W. Soergel, Gradings on representation categories, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994) (1995), 800-806, Birkhäuser, Basel Zbl0854.17006MR1403980
  13. V. V. Vershinin, On homology of virtual braids and Burau representation, J. Knot Theory Ramifications 10 (2001), 795-812 Zbl0997.57020MR1839703

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