naa a22 4500 510783759 CHVBK 20180411083255.0 cr unu---uuuuu 180411e20131001xx s 000 0 eng 10.1007/s11856-012-0180-3 doi (NATIONALLICENCE)springer-10.1007/s11856-012-0180-3 Right coideal subalgebras of Nichols algebras and the Duflo order on the Weyl groupoid [Elektronische Daten] [István Heckenberger, Hans-Jürgen Schneider] We study graded right coideal subalgebras of Nichols algebras of semisimple Yetter-Drinfeld modules. Assuming that the Yetter-Drinfeld module admits all reflections and the Nichols algebra is decomposable, we construct an injective order preserving and order reflecting map between morphisms of the Weyl groupoid and graded right coideal subalgebras of the Nichols algebra. Here morphisms are ordered with respect to right Duflo order and right coideal subalgebras are ordered with respect to inclusion. If the Weyl groupoid is finite, then we prove that the Nichols algebra is decomposable and the above map is bijective. In the special case of the Borel part of quantized enveloping algebras our result implies a conjecture of Kharchenko. Hebrew University Magnes Press, 2013 Heckenberger István Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Hans-Meerwein-Str., D-35032, Marburg, Germany aut Schneider Hans-Jürgen Mathematisches Institut, Universität München, Theresienstr. 39, D-80333, Munich, Germany aut Israel Journal of Mathematics Springer US; http://www.springer-ny.com 197/1(2013-10-01), 139-187 0021-2172 197:1<139 2013 197 11856 https://doi.org/10.1007/s11856-012-0180-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11856-012-0180-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Heckenberger István Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Hans-Meerwein-Str., D-35032, Marburg, Germany aut NATIONALLICENCE 700 1- Schneider Hans-Jürgen Mathematisches Institut, Universität München, Theresienstr. 39, D-80333, Munich, Germany aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer US; http://www.springer-ny.com 197/1(2013-10-01), 139-187 0021-2172 197:1<139 2013 197 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer