caa a22 4500 445862572 CHVBK 20180317145447.0 cr unu---uuuuu 170323e20110601xx s 000 0 eng 10.1007/s00031-011-9133-x doi (NATIONALLICENCE)springer-10.1007/s00031-011-9133-x Hopf algebra deformations of binary polyhedral groups [Elektronische Daten] [Julien Bichon, Sonia Natale] We show that semisimple Hopf algebras having a self-dual faithful irreducible comodule of dimension 2 are always obtained as abelian extensions with quotient Z2. We prove that nontrivial Hopf algebras arising in this way can be regarded as deformations of binary polyhedral groups and describe its category of representations. We also prove a strengthening of a result of Nichols and Richmond on cosemisimple Hopf algebras with a two-dimensional irreducible comodule in the finite-dimensional context. Finally, we give some applications to the classification of certain classes of semisimple Hopf algebras. Springer Science+Business Media, LLC, 2011 Bichon Julien Laboratoire de Mathématiques, Université Blaise Pascal, Complexe universitaire des Cézeaux, 63177, Aubière Cedex, France aut Natale Sonia Fa.M.A.F. -CIEM-CONICET Universidad Nacional de Córdoba, Ciudad Universitaria (5000), Córdoba, Argentina aut Transformation Groups SP Birkhäuser Verlag Boston 16/2(2011-06-01), 339-374 1083-4362 16:2<339 2011 16 31 https://doi.org/10.1007/s00031-011-9133-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00031-011-9133-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bichon Julien Laboratoire de Mathématiques, Université Blaise Pascal, Complexe universitaire des Cézeaux, 63177, Aubière Cedex, France aut NATIONALLICENCE 700 1- Natale Sonia Fa.M.A.F. -CIEM-CONICET Universidad Nacional de Córdoba, Ciudad Universitaria (5000), Córdoba, Argentina aut NATIONALLICENCE 773 0- Transformation Groups SP Birkhäuser Verlag Boston 16/2(2011-06-01), 339-374 1083-4362 16:2<339 2011 16 31 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer