Pointed Hopf algebras with triangular decomposition:A characterization of multiparameter quantum groups

Laugwitz, Robert (2016) Pointed Hopf algebras with triangular decomposition:A characterization of multiparameter quantum groups. Algebras and Representation Theory, 19 (3). pp. 547-578. ISSN 1386-923X

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Abstract

In this paper, we present an approach to the definition of multiparameter quantum groups by studying Hopf algebras with triangular decomposition. Classifying all of these Hopf algebras which are of what we call weakly separable type over a group, we obtain a class of pointed Hopf algebras which can be viewed as natural generalizations of multiparameter deformations of universal enveloping algebras of Lie algebras. These Hopf algebras are instances of a new version of braided Drinfeld doubles, which we call asymmetric braided Drinfeld doubles. This is a generalization of an earlier result by Benkart and Witherspoon (Algebr. Represent. Theory 7(3) ? BC) who showed that two-parameter quantum groups are Drinfeld doubles. It is possible to recover a Lie algebra from these doubles in the case where the group is free abelian and the parameters are generic. The Lie algebras arising are generated by Lie subalgebras isomorphic to (Formula presented.).

Item Type: Article
Uncontrolled Keywords: braided doubles,drinfeld doubles,multiparameter quantum groups,nichols–woronowicz algebras,pointed hopf algebras
Faculty \ School: Faculty of Science > School of Mathematics
Related URLs:
Depositing User: Pure Connector
Date Deposited: 06 Apr 2016 11:00
Last Modified: 11 Nov 2020 00:48
URI: https://ueaeprints.uea.ac.uk/id/eprint/58147
DOI: 10.1007/s10468-015-9588-x

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