# A note on cohomology for multiplier Hopf algebras

## TL;DR

This paper explores the extension of Hopf-cyclic cohomology to multiplier Hopf algebras by constructing cosimplicial complexes and defining modular pairs in involution, focusing on algebras over discrete groups.

## Contribution

It introduces a framework for Hopf-cyclic cohomology in the context of multiplier Hopf algebras, including new definitions and constructions.

## Key findings

- Constructed cosimplicial complexes for multiplier Hopf algebras
- Extended cyclicity operator to these complexes
- Defined Hopf-cyclic cohomology for function algebras over discrete groups

## Abstract

In this note we discuss the possibility of constructing the cosimplicial complex for the multiplier Hopf algebras and extending the cyclicity operator to obtain the Hopf-cyclic cohomology for them. We show that the definition of modular pairs in involution for multiplier Hopf algebras and provide the definition of Hopf-cyclic cohomology for algebras of functions over discrete groups.