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Abstract:

We compute the finite-dimensional Nichols algebras over the sum of two simple Yetter-Drinfeld modules V and W over non-abelian epimorphic images of a certain central extension of the dihedral group of eight elements or SL(2, 3), and such that the Weyl groupoid of the pair (V, W) is finite. These central extensions appear in the classification of non-elementary finite-dimensional Nichols algebras with finite Weyl groupoid of rank two. We deduce new information on the structure of primitive elements of finite-dimensional Nichols algebras over groups. © 2014 Elsevier Inc.

Registro:

Documento: Artículo
Título:Nichols algebras over groups with finite root system of rank two III
Autor:Heckenberger, I.; Vendramin, L.
Filiación:Philipps-Universität Marburg, FB Mathematik und Informatik, Hans-Meerwein-Straße, Marburg, 35032, Germany
Departamento de Matemática, FCEN, Universidad de Buenos Aires, Pabellón 1, Ciudad Universitaria (1428), Buenos Aires, Argentina
Palabras clave:Hopf algebras; Nichols algebras; Weyl groupoids
Año:2015
Volumen:422
Página de inicio:223
Página de fin:256
DOI: http://dx.doi.org/10.1016/j.jalgebra.2014.09.013
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_v422_n_p223_Heckenberger

Referencias:

  • Andruskiewitsch, N., Graña, M., From racks to pointed Hopf algebras (2003) Adv. Math., 178 (2), pp. 177-243
  • Andruskiewitsch, N., Heckenberger, I., Schneider, H.-J., The Nichols algebra of a semisimple Yetter-Drinfeld module (2010) Amer. J. Math., 132 (6), pp. 1493-1547
  • Cuntz, M., Heckenberger, I., Weyl groupoids of rank two and continued fractions (2009) Algebra Number Theory, 3 (3), pp. 317-340
  • 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., The Weyl groupoid of a Nichols algebra of diagonal type (2006) Invent. Math., 164 (1), pp. 175-188
  • Heckenberger, I., Schneider, H.-J., Nichols algebras over groups with finite root system of rank two I (2010) J. Algebra, 324 (11), pp. 3090-3114
  • Heckenberger, I., Schneider, H.-J., Root systems and Weyl groupoids for Nichols algebras (2010) Proc. Lond. Math. Soc. (3), 101 (3), pp. 623-654
  • Heckenberger, I., Vendramin, L., The classification of Nichols algebras with finite root system of rank two (2013) J. Eur. Math. Soc., , arxiv:1311.2881, in press
  • Heckenberger, I., Vendramin, L., Nichols algebras over groups with finite root system of rank two II (2014) J. Group Theory, , arxiv:1302.0213, in press
  • Heckenberger, I., Yamane, H., A generalization of Coxeter groups, root systems, and Matsumoto's theorem (2008) Math. Z., 259 (2), pp. 255-276

Citas:

---------- APA ----------
Heckenberger, I. & Vendramin, L. (2015) . Nichols algebras over groups with finite root system of rank two III. Journal of Algebra, 422, 223-256.
http://dx.doi.org/10.1016/j.jalgebra.2014.09.013
---------- CHICAGO ----------
Heckenberger, I., Vendramin, L. "Nichols algebras over groups with finite root system of rank two III" . Journal of Algebra 422 (2015) : 223-256.
http://dx.doi.org/10.1016/j.jalgebra.2014.09.013
---------- MLA ----------
Heckenberger, I., Vendramin, L. "Nichols algebras over groups with finite root system of rank two III" . Journal of Algebra, vol. 422, 2015, pp. 223-256.
http://dx.doi.org/10.1016/j.jalgebra.2014.09.013
---------- VANCOUVER ----------
Heckenberger, I., Vendramin, L. Nichols algebras over groups with finite root system of rank two III. J. Algebra. 2015;422:223-256.
http://dx.doi.org/10.1016/j.jalgebra.2014.09.013