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Abstract:

Using the classification of transitive groups we classify indecomposable quandles of size < 36. This classification is available in Rig, a GAP package for computations related to racks and quandles. As an application, the list of all indecomposable quandles of size < 36 not of type D is computed. © 2012 World Scientific Publishing Company.

Registro:

Documento: Artículo
Título:On the classification of quandles of low order
Autor:Vendramin, L.
Filiación:Departamento de Matemática, FCEN, Pab. I - Ciudad Universitaria, (1428), Buenos Aires, Argentina
Palabras clave:computer software; Quandles; transitive groups
Año:2012
Volumen:21
Número:9
DOI: http://dx.doi.org/10.1142/S0218216512500885
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_v21_n9_p_Vendramin

Referencias:

  • (2006) GAP - Groups, Algorithms, and Programming, Version 4.4.12, , http://www.gap-system.org, The GAP Group. Available at
  • Andruskiewitsch, N., Fantino, F., Garcia, G.A., Vendramin, L., On nichols algebras associated to simple racks (2011) Contemp. Math., 537, pp. 31-56
  • Andruskiewitsch, N., Fantino, F., Grana, M., Vendramin, L., Finite-dimensional pointed hopf algebras with alternating groups are trivial (2011) Ann. Mat. Pura Appl. (4, 190 (2), pp. 225-245
  • Andruskiewitsch, N., Fantino, F., Grana, M., Vendramin, L., Pointed hopf algebras over the sporadic simple groups (2011) J. Algebra, 325, pp. 305-320
  • Andruskiewitsch, N., Grana, M., From racks to pointed hopf algebras (2003) Adv. Math., 178 (2), pp. 177-243
  • Cannon, J.J., Holt, D.F., The transitive permutation groups of degree 32 (2008) Experiment. Math., 17 (3), pp. 307-314
  • Carter, J.S., Jelsovsky, D., Kamada, S., Langford, L., Saito, M., Quandle cohomology and state-sum invariants of knotted curves and surfaces (2003) Trans. Amer. Math. Soc., 355 (10), pp. 3947-3989
  • Clauwens, F.J.B.J., (2010) Small Connected Quandles, , preprint, arXiv:1011.2456
  • Ehrman, G., Gurpinar, A., Thibault, M., Yetter, D.N., Toward a classification of finite quandles (2008) J. Knot Theory Ramifications, 17 (4), pp. 511-520
  • Etingof, P., Soloviev, A., Guralnick, R., Indecomposable set-theoretical solutions to the quantum yang-baxter equation on a set with a prime number of elements (2001) J. Algebra, 242 (2), pp. 709-719
  • Fenn, R., Rourke, C., Racks and links in codimension two (1992) J. Knot Theory Ramifications, 1 (4), pp. 343-406
  • Fenn, R., Rourke, C., Sanderson, B., James bundles (2004) Proc. London Math. Soc. (3, 89 (1), pp. 217-240
  • Fenn, R., Rourke, C., Sanderson, B., The rack space (2007) Trans. Amer. Math. Soc., 359 (2), pp. 701-740
  • Grana, M., Heckenberger, I., Vendramin, L., Nichols algebras of group type with many quadratic relations (2011) Adv. Math., 227 (5), pp. 1956-1989
  • Grana, M., Indecomposable racks of order p2 (2004) Beiträge Algebra Geom., 45 (2), pp. 665-676
  • Ho, B., Nelson, S., Matrices and finite quandles (2005) Homology Homotopy Appl., 7 (1), pp. 197-208
  • Hulpke, A., Constructing transitive permutation groups (2005) J. Symb. Comput., 39 (1), pp. 1-30
  • Joyce, D., A classifying invariant of knots, the knot quandle (1982) J. Pure Appl. Algebra, 23 (1), pp. 37-65
  • Joyce, D., Simple quandles (1982) J. Algebra, 79 (2), pp. 307-318
  • Litherland, R.A., Nelson, S., The betti numbers of some finite racks (2003) J. Pure Appl. Algebra, 178 (2), pp. 187-202
  • Matveev, S.V., Distributive groupoids in knot theory (1982) Mat. Sb. (N.S) 119, 161 (1), pp. 78-88. , 160

Citas:

---------- APA ----------
(2012) . On the classification of quandles of low order. Journal of Knot Theory and its Ramifications, 21(9).
http://dx.doi.org/10.1142/S0218216512500885
---------- CHICAGO ----------
Vendramin, L. "On the classification of quandles of low order" . Journal of Knot Theory and its Ramifications 21, no. 9 (2012).
http://dx.doi.org/10.1142/S0218216512500885
---------- MLA ----------
Vendramin, L. "On the classification of quandles of low order" . Journal of Knot Theory and its Ramifications, vol. 21, no. 9, 2012.
http://dx.doi.org/10.1142/S0218216512500885
---------- VANCOUVER ----------
Vendramin, L. On the classification of quandles of low order. J. Knot Theory Ramifications. 2012;21(9).
http://dx.doi.org/10.1142/S0218216512500885