On the Hopf (co)center of a Hopf algebra

2015/12/11 by Chirvasitu, Alexandru, Kasprzak, Paweł · 1 citation
#16T05 #18D10 #Category Theory (math.CT) #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1512.03749

Abstract

The notion of Hopf center and Hopf cocenter of a Hopf algebra is investigated by the extension theory of Hopf algebras. We prove that each of them yields an exact sequence of Hopf algebras. Moreover the exact sequences are shown to satisfy the faithful (co)flatness condition. Hopf center and cocenter are computed for U_q(\mathfrakg) and the Hopf algebra \textrmPol(\mathbbG_q), where \mathbbG_q is the Drinfeld-Jimbo quantization of a compact semisimple simply connected Lie group \mathbbG and \mathfrakg is a simple complex Lie algebra.

Cited by

• A class of (infinite-dimensional) cosemisimple Hopf algebras constructed via abelian extensions

Related

• Hopf C*-algebras
• The ramifications of the centres: quantised function algebras at roots of unity
• Full centre of an H -module algebra
• Split extension classifiers in the category of cocommutative Hopf algebras
• Hopf formulae for cocommutative Hopf algebras