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Abstract
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This is a noticeably short biography and introductory paper on multiplier Hopf algebras.
It delves into questions regarding the signifiance of this abstract construction and the motivation
behind its creation. It also concerns quantum linear groups, especially the coordinate ring of Mq (n )
and the observation that KMq (n ) is a quadratic algebra, and can be equipped with a multiplier
Hopf ∗-algebra structure in the sense of quantum permutation groups developed by Wang and an
observation by Rollier–Vaes. In our next paper, we will propose the study of multiplier Hopf graph
algebras. The current paper can be viewed as a precursor to this upcoming work, serving as a crucial
intermediary bridging the gap between the abstract concept of multiplier Hopf algebras and the
well-developed fild of graph theory, thereby establishing connections between them! This survey
review paper is dedicated to the 78th birthday anniversary of Professor Alfons Van Daele.
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