Partial smash coproduct of multiplier Hopf algebras

Abstract

In this work, we define partial (co)actions on multiplier Hopf algebras, we also present examples and properties. From a partial comodule coalgebra, we construct a partial smash coproduct generalizing the constructions made by L. Delvaux and E. Batista and J. Vercruysse.

Keywords:

• Multiplier Hopf algebras
• partial comodule coalgebra
• partial smash coproduct

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 16T99
• Secondary: 16T15

Acknowledgment

The authors would like to thank A. Van Daele for his precious suggestions and disposition to enlighten us about the theory of Multiplier Hopf Algebras.