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Liftings of Jordan and Super Jordan Planes

Part of: Hopf algebras, quantum groups and related topics

Published online by Cambridge University Press:  12 April 2018

Nicolás Andruskiewitsch ,
Iván Angiono  and
István Heckenberger
Nicolás Andruskiewitsch*
Affiliation:
FaMAF-CIEM (CONICET), Universidad Nacional de Córdoba, Medina Allende s/n, Ciudad Universitaria, 5000 Córdoba, Argentina (andrus@famaf.unc.edu.ar; angiono@famaf.unc.edu.ar)
Iván Angiono
Affiliation:
FaMAF-CIEM (CONICET), Universidad Nacional de Córdoba, Medina Allende s/n, Ciudad Universitaria, 5000 Córdoba, Argentina (andrus@famaf.unc.edu.ar; angiono@famaf.unc.edu.ar)
István Heckenberger
Affiliation:
Philipps-Universität Marburg, Fachbereich Mathematik und Informatik, Hans-Meerwein-Strasse, D-35032 Marburg, Germany (heckenberger@mathematik.uni-marburg.de)
*
*Corresponding author.
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Abstract

We classify pointed Hopf algebras with finite Gelfand–Kirillov dimension whose infinitesimal braiding has dimension 2 but is not of diagonal type, or equivalently is a block. These Hopf algebras are new and turn out to be liftings of either a Jordan or a super Jordan plane over a nilpotent-by-finite group.

Keywords

Hopf algebrasGelfand–Kirillov dimensionJordan plane

MSC classification

Primary: 16T05: Hopf algebras and their applications
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 61 , Issue 3 , August 2018 , pp. 661 - 672
Copyright
Copyright © Edinburgh Mathematical Society 2018 

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