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Abstract:

We prove that the knot invariants given by quandles can be recovered by invariants given by traces on braided vector spaces, i.e. quantum invariants.

Registro:

Documento: Artículo
Título:Quandle knot invariants are quantum knot invariants
Autor:Graña, M.
Filiación:Depto. de Matemática, FCEyN, Ciudad Universitaria, Pab I, 1428 Buenos Aires, Argentina
Año:2002
Volumen:11
Número:5
Página de inicio:673
Página de fin:681
DOI: http://dx.doi.org/10.1142/S0218216502001883
Título revista:Journal of Knot Theory and its Ramifications
Título revista abreviado:J. Knot Theory Ramifications
ISSN:02182165
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02182165_v11_n5_p673_Grana

Referencias:

  • Fenn, R., Rourke, C., Racks and links in codimension two (1992) J. Knot Theory and Its Ramifications, 1 (4), pp. 343-406. , FR
  • Carter, J.S., Jelsovsky, D., Kamada, S., Langford, L., Saito, M., State-sum invariants of knotted curves and surfaces from quandle cohomology (1999) Electron. Res. Announc. Amer. Math. Soc., 5, pp. 146-156. , CJKLS, electronic. Also in math. GT/9903135
  • Carter, J.S., Jelsovsky, D., Kamada, S., Saito, M., Quandle homology groups, their Betti numbers, and virtual knots, , CJKS, math. GT/9909161
  • Graña, M., On Nichols algebras of low dimension (2000) Contemporary Math. N., 267. , G1, "New Trends in Hopf Algebra Theory", ed. Andruskiewitsch-Ferrer Santos-Schneider
  • Graña, M., Álgebras de Hopf punteadas y álgebras de Nichols de dimensión finita, , G2, PhD. Thesis, Univ. de Buenos Aires
  • Joyce, D., A classifying invariant of knots, the knot quandle (1982) J. Pure and Appl. Algebra, 23, pp. 37-65. , J
  • Kauffman, L., (1991) Knots and Physics, , K, World Scientific Pub. Co
  • Kauffman, L., Radford, D., A necessary and sufficient condition for a finite-dimensional Drinfel'd double to be a ribbon Hopf algebra (1993) J. Algebra, 159 (1), pp. 98-114. , KR
  • Turaev, V.G., (1994) Quantum invariants of knots and 3-manifolds, , T, W. de Gruyter, Berlin, New York

Citas:

---------- APA ----------
(2002) . Quandle knot invariants are quantum knot invariants. Journal of Knot Theory and its Ramifications, 11(5), 673-681.
http://dx.doi.org/10.1142/S0218216502001883
---------- CHICAGO ----------
Graña, M. "Quandle knot invariants are quantum knot invariants" . Journal of Knot Theory and its Ramifications 11, no. 5 (2002) : 673-681.
http://dx.doi.org/10.1142/S0218216502001883
---------- MLA ----------
Graña, M. "Quandle knot invariants are quantum knot invariants" . Journal of Knot Theory and its Ramifications, vol. 11, no. 5, 2002, pp. 673-681.
http://dx.doi.org/10.1142/S0218216502001883
---------- VANCOUVER ----------
Graña, M. Quandle knot invariants are quantum knot invariants. J. Knot Theory Ramifications. 2002;11(5):673-681.
http://dx.doi.org/10.1142/S0218216502001883