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A CLASS OF QUASITRIANGULAR GROUP-COGRADED MULTIPLIER HOPF ALGEBRAS

Part of: Lie algebras and Lie superalgebras Hopf algebras, quantum groups and related topics

Published online by Cambridge University Press:  20 December 2018

TAO YANG ,
XUAN ZHOU  and
HAIXING ZHU
TAO YANG*
Affiliation:
College of Science, Nanjing Agricultural University, Nanjing 210095, Jiangsu, China e-mail: [email protected]
XUAN ZHOU
Affiliation:
Department of Mathematics, Jiangsu Second Normal University, Nanjing 210013, Jiangsu, China e-mail: [email protected]
HAIXING ZHU
Affiliation:
College of Economics and Management, Nanjing Forestry University, Nanjing 210037, Jiangsu, China e-mail: [email protected]
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Abstract

For a multiplier Hopf algebra pairing 〈A,B〉, we construct a class of group-cograded multiplier Hopf algebras D(A,B), generalizing the classical construction of finite dimensional Hopf algebras introduced by Panaite and Staic Mihai [Isr. J. Math. 158 (2007), 349–365]. Furthermore, if the multiplier Hopf algebra pairing admits a canonical multiplier in M(B⊗A) we show the existence of quasitriangular structure on D(A,B). As an application, some special cases and examples are provided.

MSC classification

Primary: 16T05: Hopf algebras and their applications
Secondary: 17B37: Quantum groups (quantized enveloping algebras) and related deformations
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 62 , Issue 1 , January 2020 , pp. 43 - 57
Copyright
Copyright © Glasgow Mathematical Journal Trust 2018 

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