Quantum semigroups: A survey

TL;DR

This survey provides an accessible overview of quantum semigroups, emphasizing motivation and intuition, aimed at graduate students familiar with $C^*$-algebras but new to quantum groups.

Contribution

It offers a detailed, pedagogical introduction to quantum semigroups, highlighting key concepts and motivations for students and researchers entering the field.

Findings

Clarifies foundational concepts of quantum semigroups.

Provides detailed proofs and explanations.

Emphasizes motivation and intuition behind the theory.

Abstract

Notes of a 8h course given at the University of G\"oteborg during an Erasmus exchange visit, June 11-15, 2018. It is intended for PhD and graduate students familiar with $C^*$-algebras but not specializing in quantum groups. The proofs, if included, are presented in detail, but most facts are not proved. A special emphasis is put onto motivation of the theory and the intuition behind.