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Mat. Sb., 2001, Volume 192, Number 5, Pages 53–64 (Mi msb564)  

This article is cited in 20 scientific papers (total in 20 papers)

On braid groups

T. V. Dubrovina, N. I. Dubrovin

Vladimir State University

Abstract: Artin's braid groups are studied from the viewpoint of right-ordered groups. A right order is constructed such that the cone of elements $\geqslant 1$ is finitely generated as a monoid. The structure of ideals of this cone is determined, and it turns out to be quite specific and impossible for linearly ordered groups. It is also proved that no linear order on the pure braid subgroup can be extended to a right order on the whole of the braid group.

DOI: https://doi.org/10.4213/sm564

Full text: PDF file (242 kB)
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English version:
Sbornik: Mathematics, 2001, 192:5, 693–703

Bibliographic databases:

UDC: 512.8
MSC: Primary 20F36; Secondary 06F15, 20F60
Received: 24.01.2000

Citation: T. V. Dubrovina, N. I. Dubrovin, “On braid groups”, Mat. Sb., 192:5 (2001), 53–64; Sb. Math., 192:5 (2001), 693–703

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. Ya. Medvedev, “Orders on Braid Groups”, Algebra and Logic, 42:3 (2003), 177–180  mathnet  crossref  mathscinet  zmath  elib
    2. Andrés Navas, Cristóbal Rivas, “A new characterization of Conrad's property for group orderings, with applications”, Algebr Geom Topol, 9:4 (2009), 2079  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    3. Navas A., “On the Dynamics of (Left) Orderable Groups”, Annales de l Institut Fourier, 60:5 (2010), 1685–1740  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    4. Clay A., “Isolated points in the space of left orderings of a group”, Groups Geometry and Dynamics, 4:3 (2010), 517–532  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    5. Cristóbal Rivas, “Left-orderings on free products of groups”, Journal of Algebra, 2011  crossref  mathscinet  isi  scopus  scopus  scopus
    6. Andrés Navas, “A remarkable family of left-ordered groups: Central extensions of Hecke groups”, Journal of Algebra, 328:1 (2011), 31  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    7. Navas A., Wiest B., “Nielsen-Thurston orders and the space of braid orderings”, Bull London Math Soc, 43:5 (2011), 901–911  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    8. Cristóbal Rivas, “On Groups with Finitely Many Conradian Orderings”, Communications in Algebra, 40:7 (2012), 2596  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    9. Clay A., “Free Lattice-Ordered Groups and the Space of Left Orderings”, Mon.heft. Math., 167:3-4 (2012), 417–430  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    10. Clay A., “Left Orderings and Quotients of the Braid Groups”, J. Knot Theory Ramifications, 21:14 (2012), 1250130  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    11. Tetsuya Ito, “Dehornoy-like left orderings and isolated left orderings”, Journal of Algebra, 374 (2013), 42  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    12. Adam Clay, Tye Lidman, Liam Watson, “Graph manifolds, left-orderability and amalgamation”, Algebr. Geom. Topol, 13:4 (2013), 2347  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    13. Rolfsen D., “Low-Dimensional Topology and Ordering Groups”, Math. Slovaca, 64:3 (2014), 579–600  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    14. Dehornoy P., “Monoids of O-Type, Subword Reversing, and Ordered Groups”, J. Group Theory, 17:3 (2014), 465–524  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    15. Linnell P., Morris D.W., “Amenable Groups With a Locally Invariant Order Are Locally Indicable”, Group. Geom. Dyn., 8:2 (2014), 467–478  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    16. Ito T., “Construction of isolated left orderings via partially central cyclic amalgamation”, Tohoku Math. J., 68:1 (2016), 49–71  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    17. Rivas C., Tessera R., “On the space of left-orderings of virtually solvable groups”, Group. Geom. Dyn., 10:1 (2016), 65–90  crossref  mathscinet  zmath  isi  scopus
    18. Ito T., “Isolated Orderings on Amalgamated Free Products”, Group. Geom. Dyn., 11:1 (2017), 121–138  crossref  mathscinet  zmath  isi  scopus
    19. Hermiller S., Sunic Z., “No Positive Cone in a Free Product Is Regular”, Int. J. Algebr. Comput., 27:8 (2017), 1113–1120  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    20. Arcis D., Paris L., “Ordering Garside Groups”, Int. J. Algebr. Comput., 29:5 (2019), 861–883  crossref  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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