V. F. R. Jones :
“Quantum mechanics over fields of non-zero characteristic ,”
Lett. Math. Phys.
1 : 2
(1975–1976 ),
pp. 99–103 .
MR
418670
article
Abstract
BibTeX
@article {key418670m,
AUTHOR = {Jones, V. F. R.},
TITLE = {Quantum mechanics over fields of non-zero
characteristic},
JOURNAL = {Lett. Math. Phys.},
FJOURNAL = {Letters in Mathematical Physics},
VOLUME = {1},
NUMBER = {2},
YEAR = {1975--1976},
PAGES = {99--103},
DOI = {10.1007/BF00398370},
NOTE = {MR:418670.},
ISSN = {0377-9017},
}
V. F. R. Jones :
Actions of finite groups on the hyperfinite type \( \mathrm{II}_1 \) factor .
Memoirs of the American Mathematical Society 237 .
American Matheammatical Society (Providence, RI ),
1980 .
Republication of Jones’ 1979 PhD thesis .
MR
587749
Zbl
0454.46045
book
BibTeX
@book {key587749m,
AUTHOR = {Jones, Vaughan F. R.},
TITLE = {Actions of finite groups on the hyperfinite
type \$\mathrm{II}_1\$ factor},
SERIES = {Memoirs of the American Mathematical
Society},
NUMBER = {237},
PUBLISHER = {American Matheammatical Society},
ADDRESS = {Providence, RI},
YEAR = {1980},
PAGES = {v+70},
DOI = {10.1090/memo/0237},
NOTE = {Republication of Jones' 1979 PhD thesis.
MR:587749. Zbl:0454.46045.},
ISSN = {0065-9266},
ISBN = {9780821822371},
}
V. F. R. Jones :
“L’indice d’un sous-facteur d’un facteur de type \( \mathrm{II} \) ”
[The index of a subfactor of a type \( \mathrm{II} \) factor ],
C. R. Acad. Sci. Paris Sér. I Math.
294 : 12
(1982 ),
pp. 391–394 .
MR
659729
Zbl
0492.46048
article
BibTeX
@article {key659729m,
AUTHOR = {Jones, Vaughan F. R.},
TITLE = {L'indice d'un sous-facteur d'un facteur
de type \$\mathrm{II}\$ [The index of
a subfactor of a type \$\mathrm{II}\$
factor]},
JOURNAL = {C. R. Acad. Sci. Paris S\'er. I Math.},
FJOURNAL = {Comptes Rendus des S\'eances de l'Acad\'emie
des Sciences. S\'erie I. Math\'ematique},
VOLUME = {294},
NUMBER = {12},
YEAR = {1982},
PAGES = {391--394},
NOTE = {MR:659729. Zbl:0492.46048.},
ISSN = {0249-6291},
}
V. F. R. Jones :
“Index for subfactors ,”
Invent. Math.
72 : 1
(1983 ),
pp. 1–25 .
A lecture based on this was published in Fields Medallists’ lectures (1997) .
MR
696688
Zbl
0508.46040
article
BibTeX
@article {key696688m,
AUTHOR = {Jones, V. F. R.},
TITLE = {Index for subfactors},
JOURNAL = {Invent. Math.},
FJOURNAL = {Inventiones Mathematicae},
VOLUME = {72},
NUMBER = {1},
YEAR = {1983},
PAGES = {1--25},
DOI = {10.1007/BF01389127},
NOTE = {A lecture based on this was published
in \textit{Fields Medallists' lectures}
(1997). MR:696688. Zbl:0508.46040.},
ISSN = {0020-9910},
}
V. F. R. Jones :
“A polynomial invariant for knots via von Neumann algebras ,”
Bull. Am. Math. Soc.
12 : 1
(January 1985 ),
pp. 103–111 .
A lecture based on this was published in Fields Medallists’ lectures (1997) .
MR
766964
Zbl
0564.57006
article
BibTeX
@article {key766964m,
AUTHOR = {Jones, V. F. R.},
TITLE = {A polynomial invariant for knots via
von {N}eumann algebras},
JOURNAL = {Bull. Am. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical
Society},
VOLUME = {12},
NUMBER = {1},
MONTH = {January},
YEAR = {1985},
PAGES = {103--111},
DOI = {10.1090/S0273-0979-1985-15304-2},
NOTE = {A lecture based on this was published
in \textit{Fields Medallists' lectures}
(1997). MR:766964. Zbl:0564.57006.},
ISSN = {0273-0979},
}
V. Jones :
“A new knot polynomial and von Neumann algebras ,”
Notices Am. Math. Soc.
33 : 2
(March 1986 ),
pp. 219–225 .
MR
830613
article
BibTeX
@article {key830613m,
AUTHOR = {Jones, Vaughan},
TITLE = {A new knot polynomial and von {N}eumann
algebras},
JOURNAL = {Notices Am. Math. Soc.},
FJOURNAL = {Notices of the American Mathematical
Society},
VOLUME = {33},
NUMBER = {2},
MONTH = {March},
YEAR = {1986},
PAGES = {219--225},
NOTE = {MR:830613.},
ISSN = {0002-9920},
}
V. F. R. Jones :
“Hecke algebra representations of braid groups and link polynomials ,”
Ann. Math. (2)
126 : 2
(September 1987 ),
pp. 335–388 .
This was republished in New Developments in the Theory of Knots (1990) .
MR
908150
Zbl
0631.57005
article
Abstract
BibTeX
By studying representations of the braid group satisfying a certain quadratic relation we obtain a polynomial invariant in two variables for oriented links. It is expressed using a trace, discovered by Ocneanu, on the Hecke algebras of type A. A certain specialization of the polynomial, whose discovery predated and inspired the two-variable one, is seen to come in two inequivalent ways, from a Hecke algebra quotient and a linear functional on it which has already been used in statistical mechanics. The two-variable polynomial was first discovered by Freyd–Yetter, Lickorish–Millet, Ocneanu, Hoste, and Przytycki–Traczyk.
@article {key908150m,
AUTHOR = {Jones, V. F. R.},
TITLE = {Hecke algebra representations of braid
groups and link polynomials},
JOURNAL = {Ann. Math. (2)},
FJOURNAL = {Annals of Mathematics. Second Series},
VOLUME = {126},
NUMBER = {2},
MONTH = {September},
YEAR = {1987},
PAGES = {335--388},
DOI = {10.2307/1971403},
NOTE = {This was republished in \textit{New
Developments in the Theory of Knots}
(1990). MR:908150. Zbl:0631.57005.},
ISSN = {0003-486X},
}
V. F. R. Jones :
Planar algebras, I .
Preprint ,
Department of Mathematics, University of California, Berkeley ,
1999 .
ArXiv
math/9909027v1
techreport
BibTeX
@techreport {keymath/9909027v1a,
AUTHOR = {V. F. R. Jones},
TITLE = {Planar algebras, I},
TYPE = {preprint},
INSTITUTION = {Department of Mathematics, University
of California, Berkeley},
YEAR = {1999},
NOTE = {ArXiv:math/9909027v1.},
}
V. F. R. Jones :
“The annular structure of subfactors ,”
pp. 401–463
in
Essays on geometry and related topics: Mémoires dédiés à André Haefliger
[Essays on geometry and related topics: Memoirs dedicated to André Haefliger ],
vol. 2 .
Edited by É. Ghys, P. de la Harpe, V. F. R. Jones, V. Sergiescu, and T. Tsuboi .
Monographies de l’Enseignement Mathématique 38 .
Enseignement Mathématique (Geneva ),
2001 .
MR
1929335
Zbl
1019.46036
ArXiv
math/0105071
incollection
Abstract
People
BibTeX
Given a planar algebra we show the equivalence of the notions of a module over this algebra (in the operadic sense), and module over a universal annular algebra. We classify such modules, with invariant inner products, in the generic region and give applications to subfactors, including a planar construction of the \( E_6 \) and \( E_8 \) subfactors.
@incollection {key1929335m,
AUTHOR = {Jones, Vaughan F. R.},
TITLE = {The annular structure of subfactors},
BOOKTITLE = {Essays on geometry and related topics:
{M}\'emoires d\'edi\'es \`a {A}ndr\'e
{H}aefliger [Essays on geometry and
related topics: {M}emoirs dedicated
to {A}ndr\'e {H}aefliger]},
EDITOR = {Ghys, \'Etienne and de la Harpe, Pierre
and Jones, Vaughan F. R. and Sergiescu,
Vlad and Tsuboi, Takashi},
VOLUME = {2},
SERIES = {Monographies de l'Enseignement Math\'ematique},
NUMBER = {38},
PUBLISHER = {Enseignement Math\'ematique},
ADDRESS = {Geneva},
YEAR = {2001},
PAGES = {401--463},
NOTE = {ArXiv:math/0105071. MR:1929335. Zbl:1019.46036.},
ISSN = {0425-0818},
ISBN = {9782940264049},
}
V. F. R. Jones and F. Xu :
“Intersections of finite families of finite index subfactors ,”
Int. J. Math.
15 : 7
(2004 ),
pp. 717–733 .
MR
2085101
Zbl
1059.46043
ArXiv
math/0406331
article
Abstract
People
BibTeX
@article {key2085101m,
AUTHOR = {Jones, Vaughan F. R. and Xu, Feng},
TITLE = {Intersections of finite families of
finite index subfactors},
JOURNAL = {Int. J. Math.},
FJOURNAL = {International Journal of Mathematics},
VOLUME = {15},
NUMBER = {7},
YEAR = {2004},
PAGES = {717--733},
DOI = {10.1142/S0129167X04002521},
NOTE = {ArXiv:math/0406331. MR:2085101. Zbl:1059.46043.},
ISSN = {0129-167X},
}
T. Evans and V. F. R. Jones :
A conversation with Sir Vaughan Jones, New Zealand mathematician and Fields medalist ,
2016 .
Video interview, University of Auckland.
misc
BibTeX
@misc {key87573033,
AUTHOR = {T. Evans and V. F. R. Jones},
TITLE = {A conversation with Sir Vaughan Jones,
New Zealand mathematician and Fields
medalist},
HOWPUBLISHED = {Video interview, University of Auckland},
YEAR = {2016},
URL = {https://www.youtube.com/watch?v=caJ0jYHOS8g},
}
V. Jones :
“Some unitary representations of Thompson’s groups \( F \) and \( T \) ,”
J. Comb. Algebra
1 : 1
(2017 ),
pp. 1–44 .
MR
3589908
Zbl
06684911
ArXiv
1412.7740
article
Abstract
BibTeX
In a “naive” attempt to create algebraic quantum field theories on the circle, we obtain a family of unitary representations of Thompson’s groups \( T \) and \( F \) for any subfactor. The Thompson group elements are the “local scale transformations” of the theory. In a simple case the coefficients of the representations are polynomial invariants of links. We show that all links arise and introduce new “oriented” subgroups of
\( \vec{F} < F \) and \( \vec{T} < T \)
which allow us to produce all oriented knots and links.
@article {key3589908m,
AUTHOR = {Jones, Vaughan},
TITLE = {Some unitary representations of {T}hompson's
groups \$F\$ and \$T\$},
JOURNAL = {J. Comb. Algebra},
FJOURNAL = {Journal of Combinatorial Algebra},
VOLUME = {1},
NUMBER = {1},
YEAR = {2017},
PAGES = {1--44},
DOI = {10.4171/JCA/1-1-1},
NOTE = {ArXiv:1412.7740. MR:3589908. Zbl:06684911.},
ISSN = {2415-6302},
}
V. F. R. Jones :
“Correspondence with Vaughan Jones ,”
Celebratio Mathematica
(2019 ).
article
People
BibTeX
@article {key80160786,
AUTHOR = {Jones, V. F. R},
TITLE = {Correspondence with Vaughan Jones},
JOURNAL = {Celebratio Mathematica},
YEAR = {2019},
URL = {https://celebratio.org/Birman_JS/article/639/},
}