On nichols algebras over PGL (2, q) and PSL (2, q)

Mostrar otras versiones (1)

We compute necessary conditions on YetterDrinfeld modules over the groups PGL(2, q) = PGL(2, q) and PSL(2, q) = PSL(2, q) to generate finite-dimensional Nichols algebras. This is a first step towards a classification of pointed Hopf algebras with group of group-likes isomorphic to one of these group...

Descripción completa

Guardado en:
Detalles Bibliográficos
Autor principal: Freyre, S.
Otros Autores: Graña, M., Vendramin, L.
Formato: Capítulo de libro
Lenguaje:Inglés
Publicado: 2010
Acceso en línea:Registro en Scopus
DOI
Handle
Registro en la Biblioteca Digital
Aporte de:Registro referencial: Solicitar el recurso aquí
Biblioteca Central Dr. Luis F. Leloir (FCEN) de Universidad de Buenos Aires
LEADER 06182caa a22006137a 4500
001 PAPER-7977
003 AR-BaUEN
005 20230518203745.0
008 190411s2010 xx ||||fo|||| 00| 0 eng|d
024 7 |2 scopus  |a 2-s2.0-77951669105 
040 |a Scopus  |b spa  |c AR-BaUEN  |d AR-BaUEN 
100 1 |a Freyre, S. 
245 1 3 |a On nichols algebras over PGL (2, q) and PSL (2, q) 
260 |c 2010 
270 1 0 |m Freyre, S.; Departamento de Matemática - FCEyN, Universidad de Buenos Aires, PAB i - Ciudad Universitaria, (1428) Buenos Aires, Argentina; email: sfreyre@dm.uba.ar 
506 |2 openaire  |e Política editorial 
504 |a Alperin, J.L., Bell, R., Groups and representations (1995) Graduate Texts in Mathematics, 162. , Springer-Verlag, New York 
504 |a Adams, J., Characters Tables of GL (2, Q), SL (2, Q), PGL (2, Q) and PSL (2, q), , http://www.math.umd.edu/~jda/characters/2002 
504 |a Andruskiewitsch, N., Fantino, F., On pointed hopf algebras associated with alternating and dihedral groups (2007) Rev. Unión Mat. Argent., 48 (3), pp. 57-71 
504 |a Andruskiewitsch, N., Fantino, F., On pointed hopf algebras associated with unmixed conjugacy classes (2007) J. Math. Phys., 48 (3), p. 033502. , in Sm 
504 |a Andruskiewitsch, N., Fantino, F., Graña, M., Vendramin, L., Pointed Hopf Algebras Over Alternating Groups Are Trivial, , arXiv:00812.4628v3 
504 |a Andruskiewitsch, N., Graña, M., Braided hopf algebras over non-abelian finite groups (1999) Bol. Acad. Nac. Cienc, 63, pp. 45-78. , Córdoba, Colloquium on Operator Algebras and Quantum Groups Spanish Vaquerías, 1997 
504 |a Andruskiewitsch, N., Schneider, H.-J., Pointed hopf algebras (2002) New Directions in Hopf Algebras, 43. , in, 1-68, Math. Sci. Res. Inst. Publ, Cambridge Univ. Press, Cambridge 
504 |a Andruskiewitsch, N., Zhang, S., On pointed hopf algebras associated to some con-jugacy classes (2007) Proc. Amer. Math. Soc., 135 (9), pp. 2723-2731. , in Sn, electronic 
504 |a Conway, J.H., Curtis, R.T., Norton, S.P., Parker, R.A., Wilson, R.A., Atlas of Finite Groups, , Oxford University Press, Eynsham, 1985 Maximal subgroups and ordinary characters for simple groups, with computational assistance from J. G. Thackray 
504 |a Dickson, L., (1958) Linear Groups: With an Exposition of the Galois Field Theory, , Dover Publications Inc., New York 
504 |a Fantino, F., On pointed hopf algebras associated with the mathieu simple groups (2009) J. Algebra Appl., 5, pp. 633-672 
504 |a Freyre, S., Graña, M., Vendramin, L., On nichols algebras over SL (2, Fq) and GL (2, Fq) (2007) J. Math. Phys., 48 (12), p. 123513. , 24 pages 
504 |a (2006), http://www.gap-system.org, GAP Group, GAP - Groups, Algorithms, and Programming, Version 4.4.9; Gorenstein, D., (1968) Finite Groups, , Harper & Row Publishers, New York 
504 |a Graña, M., Nichols Algebras of Nonabelian Group Type, , http://mate.dm.uba.ar/~matiasg/zoo.html, web page at 
504 |a Heckenberger, I., Classification of arithmetic root systems of rank 3 (2005) Actas of XVI Colloquium Latinoamericano De Álgebra 
504 |a Heckenberger, I., The Weyl groupoid of a Nichols algebra of diagonal type (2006) Inventiones Mathematicae, 164 (1), pp. 175-188. , DOI 10.1007/s00222-005-0474-8 
504 |a Heckenberger, I., Classification of arithmetic root systems (2009) Adv. Math., 220, pp. 59-124 
504 |a Huppert, B., Endliche gruppen. I, die grundlehren der mathematischen wis-senschaften (1967) Band, 134. , Springer-Verlag, Berlin 
504 |a Serre, J.-P., (1977) Linear Representations of Finite Groups, 42. , Springer-Verlag, New York, Translated from the second French edition by L. L. Scott, Graduate Texts in Mathematics 
504 |a Wilson, R., Walsh, P., Tripp, J., Suleiman, I., Parker, R., Norton, S., Nickerson, S., Abbott, R., Atlas of Finite Group Representations, , http://brauer.maths.qmul.ac.uk/Atlas/v3/, Version 3 
520 3 |a We compute necessary conditions on YetterDrinfeld modules over the groups PGL(2, q) = PGL(2, q) and PSL(2, q) = PSL(2, q) to generate finite-dimensional Nichols algebras. This is a first step towards a classification of pointed Hopf algebras with group of group-likes isomorphic to one of these groups. As a by-product of the techniques developed in this work, we prove that any finite-dimensional pointed Hopf algebra over the Mathieu groups M20 or M21 = PSL(3, 4) is the group algebra. © 2010 World Scientific Publishing Company.  |l eng 
536 |a Detalles de la financiación: Consejo Nacional de Investigaciones Científicas y Técnicas, CONICET 
536 |a Detalles de la financiación: We thank Nicolás Andruskiewitsch and Fernando Fantino for fruitful discussions. We have used GAP [13] to do some of the computations. This work was partially supported by CONICET and ANPCyT (Argentina). 
593 |a Departamento de Matemática - FCEyN, Universidad de Buenos Aires, PAB i - Ciudad Universitaria, (1428) Buenos Aires, Argentina 
593 |a Instituto de Ciencias, Universidad Nacional General Sarmiento, J. M. Gutierrez 1150 - Los Polvorines (1613), Provincia de Buenos Aires, Argentina 
690 1 0 |a NICHOLS ALGEBRA 
690 1 0 |a POINTED HOPF ALGEBRA 
690 1 0 |a RACKS 
700 1 |a Graña, M. 
700 1 |a Vendramin, L. 
773 0 |d 2010  |g v. 9  |h pp. 195-208  |k n. 2  |p J. Algebra Appl.  |x 02194988  |w (AR-BaUEN)CENRE-5398  |t Journal of Algebra and its Applications 
856 4 1 |u https://www.scopus.com/inward/record.uri?eid=2-s2.0-77951669105&doi=10.1142%2fS0219498810003823&partnerID=40&md5=767dbc2a508b8991e4650816c59ee427  |y Registro en Scopus 
856 4 0 |u https://doi.org/10.1142/S0219498810003823  |y DOI 
856 4 0 |u https://hdl.handle.net/20.500.12110/paper_02194988_v9_n2_p195_Freyre  |y Handle 
856 4 0 |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02194988_v9_n2_p195_Freyre  |y Registro en la Biblioteca Digital 
961 |a paper_02194988_v9_n2_p195_Freyre  |b paper  |c PE 
962 |a info:eu-repo/semantics/article  |a info:ar-repo/semantics/artículo  |b info:eu-repo/semantics/publishedVersion 
999 |c 68930 

Ejemplares similares