Artículo

García Iglesias, A.; Vendramin, L."An explicit description of the second cohomology group of a quandle" (2017) Mathematische Zeitschrift. 286(3-4):1041-1063
Estamos trabajando para incorporar este artículo al repositorio
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

We use the inflation-restriction sequence and a result of Etingof and Graña on the rack cohomology to give a explicit description of 2-cocycles of finite indecomposable quandles with values in an abelian group. Several applications are given. © 2016, Springer-Verlag Berlin Heidelberg.

Registro:

Documento: Artículo
Título:An explicit description of the second cohomology group of a quandle
Autor:García Iglesias, A.; Vendramin, L.
Filiación:FaMAF–CIEM (CONICET), Universidad Nacional de Córdoba, Medina Allende s/n, Ciudad Universitaria (5000), Córdoba, Argentina
Departamento de Matemática – FCEN, Universidad de Buenos Aires, Pabellón I, Ciudad Universitaria (1428), Buenos Aires, Argentina
Año:2017
Volumen:286
Número:3-4
Página de inicio:1041
Página de fin:1063
DOI: http://dx.doi.org/10.1007/s00209-016-1794-7
Handle:http://hdl.handle.net/20.500.12110/paper_00255874_v286_n3-4_p1041_GarciaIglesias
Título revista:Mathematische Zeitschrift
Título revista abreviado:Math. Z.
ISSN:00255874
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255874_v286_n3-4_p1041_GarciaIglesias

Referencias:

  • Andruskiewitsch, N., Fantino, F., García, G.A., Vendramin, L., Milies, C.P., On Nichols algebras associated to simple racks (2011) Groups, Algebras and Applications, volume 537 of Contemporary Mathematics, pp. 31-56. , American Mathematical Society, Providence, RI
  • Andruskiewitsch, N., Graña, M., From racks to pointed Hopf algebras (2003) Adv. Math, 178 (2), pp. 177-243
  • Brown, K.S., Cohomology of Groups, volume 87 of Graduate Texts in Mathematics. Springer, New York (1994) Corrected reprint of the 1982 original
  • 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
  • Carter, J.S., Jelsovsky, D., Kamada, S., Saito, M., Quandle homology groups, their Betti numbers, and virtual knots (2001) J. Pure Appl. Algebra, 157 (2-3), pp. 135-155
  • Clark, W.E., Elhamdadi, M., Saito, M., Yeatman, T., Quandle colorings of knots and applications (2014) J. Knot Theory Ramif, 23 (6), p. 1450035
  • Clauwens, F.J.B.J., The Adjoint Group of an Alexander Quandle, , Preprint: arXiv:1011.1587
  • Eisermann, M., Quandle coverings and their Galois correspondence (2014) Fund. Math, 225, pp. 103-168
  • Etingof, P., Graña, M., On rack cohomology (2003) J. Pure Appl. Algebra, 177 (1), pp. 49-59
  • Fenn, R., Rourke, C., Sanderson, B., Trunks and classifying spaces (1995) Appl. Categ. Structures, 3 (4), pp. 321-356
  • Fenn, R., Rourke, C., Sanderson, B., James bundles (2004) Proc. Lond. Math. Soc. (3), 89 (1), pp. 217-240
  • Graña, M., Andruskiewitsch, N., Ferrer Santos, W.R., Schneider, H.-J., On Nichols algebras of low dimension (2000) New Trends in Hopf Algebra Theory (La Falda, 1999), volume 267 of Contemp. Math, pp. 111-134. , Amer. Math. Soc., Providence, RI
  • Graña, M., Indecomposable racks of order p2 (2004) Beiträge Algebra Geom, 45 (2), pp. 665-676
  • Graña, M., Heckenberger, I., Vendramin, L., Nichols algebras of group type with many quadratic relations (2011) Adv. Math, 227 (5), pp. 1956-1989
  • Heckenberger, I., Vendramin, L., Nichols algebras over groups with finite root system of rank two II (2014) J. Group Theory, 17 (6), pp. 1009-1034
  • Hulpke, A., Stanovský, D., Vojtěchovský, P., Connected quandles and transitive groups (2016) J. Pure Appl. Algebra, 220 (2), pp. 735-758
  • Joyce, D., A classifying invariant of knots, the knot quandle (1982) J. Pure Appl. Algebra, 23 (1), pp. 37-65
  • Lebed, V., Homologies of algebraic structures via braidings and quantum shuffles (2013) J. Algebra, 391, pp. 152-192
  • 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), 160, pp. 78-88
  • Milinski, A., Schneider, H.-J., Andruskiewitsch, N., Ferrer Santos, W.R., Schneider, H.-J., Pointed indecomposable Hopf algebras over Coxeter groups (2000) New trends in Hopf Algebra Theory (La Falda, 1999), volume 267 of Contemporary Mathematics, pp. 215-236. , American Mathematical Society, Providence, RI
  • Nosaka, T., Quandle homotopy invariants of knotted surfaces (2013) Math. Z, 274 (1-2), pp. 341-365
  • Rotman, J.J., (1995) An introduction to the theory of groups, volume 148 of Graduate Texts in Mathematics. Springer, New York
  • Stanovský, D., A guide to self-distributive quasigroups, or Latin quandles (2015) Quasigroups Relat. Syst, 23 (1), pp. 91-128
  • Tamaru, H., Two-point homogeneous quandles with prime cardinality (2013) J. Math. Soc. Jpn, 65 (4), pp. 1117-1134

Citas:

---------- APA ----------
García Iglesias, A. & Vendramin, L. (2017) . An explicit description of the second cohomology group of a quandle. Mathematische Zeitschrift, 286(3-4), 1041-1063.
http://dx.doi.org/10.1007/s00209-016-1794-7
---------- CHICAGO ----------
García Iglesias, A., Vendramin, L. "An explicit description of the second cohomology group of a quandle" . Mathematische Zeitschrift 286, no. 3-4 (2017) : 1041-1063.
http://dx.doi.org/10.1007/s00209-016-1794-7
---------- MLA ----------
García Iglesias, A., Vendramin, L. "An explicit description of the second cohomology group of a quandle" . Mathematische Zeitschrift, vol. 286, no. 3-4, 2017, pp. 1041-1063.
http://dx.doi.org/10.1007/s00209-016-1794-7
---------- VANCOUVER ----------
García Iglesias, A., Vendramin, L. An explicit description of the second cohomology group of a quandle. Math. Z. 2017;286(3-4):1041-1063.
http://dx.doi.org/10.1007/s00209-016-1794-7