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Abstract:

We define the fundamental group of a Hopf algebra over a field. For this purpose we first consider gradings of Hopf algebras and Galois coverings. The latter are given by linear categories with new additional structure which we call Hopf linear categories over a finite group. We compare this invariant to the fundamental group of the underlying linear category, and we compute those groups for families of examples. © 2016 Elsevier Inc.

Registro:

Documento: Artículo
Título:The fundamental group of a Hopf linear category
Autor:Cibils, C.; Solotar, A.
Filiación:Institut Montpelliérain Alexander Grothendieck (IMAG), UMR 5149, Université de Montpellier, Montpellier cedex 5, F-34095, France
IMAS-CONICET y Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón 1, Buenos Aires, 1428, Argentina
Palabras clave:Fundamental group; Grading; Hopf category
Año:2016
Volumen:462
Página de inicio:137
Página de fin:162
DOI: http://dx.doi.org/10.1016/j.jalgebra.2016.04.031
Título revista:Journal of Algebra
Título revista abreviado:J. Algebra
ISSN:00218693
CODEN:JALGA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v462_n_p137_Cibils

Referencias:

  • Aguiar, M., Mahajan, S., Hopf monoids in the category of species (2013) Contemp. Math., 585, pp. 17-124. , Amer. Math. Soc., Providence, RI, Hopf Algebras and Tensor Categories
  • Bahturin, Y.A., Zaicev, M.V., Group gradings on simple Lie algebras of type A (2006) J. Lie Theory, 16, pp. 719-742
  • Beneish, E., Chin, W., Coverings of graded pointed Hopf algebras (2015) J. Algebra, 422, pp. 730-740
  • Cibils, C., A quiver quantum group (1993) Comm. Math. Phys., 157, pp. 459-477
  • Cibils, C., Marcos, E., Skew category, Galois covering and smash product of a category over a ring (2006) Proc. Amer. Math. Soc., 134, pp. 39-50
  • Cibils, C., Redondo, M.J., Solotar, A., Connected gradings and fundamental group (2010) Algebra Number Theory, 4, pp. 625-648
  • Cibils, C., Redondo, M.J., Solotar, A., Fundamental group of Schurian categories and the Hurewicz isomorphism (2011) Doc. Math., 16, pp. 581-595
  • Cibils, C., Redondo, M.J., Solotar, A., The intrinsic fundamental group of a linear category (2012) Algebr. Represent. Theory, 15, pp. 735-753
  • Cibils, C., Redondo, M.J., Solotar, A., On universal gradings, versal gradings and Schurian generated categories (2014) J. Noncommut. Geom., 8, pp. 1101-1122
  • Cibils, C., Rosso, M., Algèbres des chemins quantiques (1997) Adv. Math., 125, pp. 171-199
  • Cibils, C., Rosso, M., Hopf quivers (2002) J. Algebra, 254, pp. 241-251
  • Dăscălescu, S., Group gradings on diagonal algebras (2008) Arch. Math. (Basel), 91, pp. 212-217
  • Douady, R., Douady, A., (2005) Algèbre et théories galoisiennes, p. 448. , Cassini, Paris
  • Elduque, A., Fine gradings on simple classical Lie algebras (2010) J. Algebra, 324, pp. 3532-3571
  • Gerstenhaber, M., Schack, S.D., Bialgebra cohomology, deformations, and quantum groups (1990) Proc. Natl. Acad. Sci. USA, 87, pp. 478-481
  • Ginosar, Y., Schnabel, O., Groups of central type, maximal connected gradings and intrinsic fundamental groups of complex semisimple algebras, , arxiv:1602.06694
  • Hatcher, A., (2002) Algebraic Topology, p. 544. , Cambridge University Press, Cambridge
  • Kac, V., (1990) Infinite Dimensional Lie Algebras, , Cambridge University Press, Cambridge
  • Kochetov, M., Gradings on finite-dimensional simple Lie algebras (2009) Acta Appl. Math., 108, pp. 101-127
  • Mac Lane, S., Categories for the Working Mathematician (1998) Grad. Texts in Math., 5. , Springer-Verlag, New York
  • Montgomery, S., Hopf Algebras and Their Actions on Rings (1993) CBMS Reg. Conf. Ser. Math., 82, pp. 14 and 238. , American Mathematical Society, Providence, RI. Published for the Conference Board of the Mathematical Sciences, Washington, DC
  • Pagon, D., Repovš, D., Zaicev, M., Group gradings on finite dimensional Lie algebras (2013) Algebra Colloq., 20, pp. 573-578
  • Patras, F., L'algèbre des descentes d'une bigèbre graduée (1994) J. Algebra, 170, pp. 547-566
  • Taillefer, R., Cohomology theories of Hopf bimodules and cup-product (2004) Algebr. Represent. Theory, 7, pp. 471-490
  • Turaev, V., Crossed group-categories (2008) Arab. J. Sci. Eng. Sect. C Theme Issues, 33, pp. 483-503
  • Turaev, V., Homotopy field theory in dimension 3 and crossed group-categories, , arxiv:math/0005291, preprint
  • Virelizier, A., Hopf group-coalgebras (2002) J. Pure Appl. Algebra, 171, pp. 75-122

Citas:

---------- APA ----------
Cibils, C. & Solotar, A. (2016) . The fundamental group of a Hopf linear category. Journal of Algebra, 462, 137-162.
http://dx.doi.org/10.1016/j.jalgebra.2016.04.031
---------- CHICAGO ----------
Cibils, C., Solotar, A. "The fundamental group of a Hopf linear category" . Journal of Algebra 462 (2016) : 137-162.
http://dx.doi.org/10.1016/j.jalgebra.2016.04.031
---------- MLA ----------
Cibils, C., Solotar, A. "The fundamental group of a Hopf linear category" . Journal of Algebra, vol. 462, 2016, pp. 137-162.
http://dx.doi.org/10.1016/j.jalgebra.2016.04.031
---------- VANCOUVER ----------
Cibils, C., Solotar, A. The fundamental group of a Hopf linear category. J. Algebra. 2016;462:137-162.
http://dx.doi.org/10.1016/j.jalgebra.2016.04.031