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From Quantum Automorphism of (Directed) Graphs to the Associated Multiplier Hopf Algebras

Author

Listed:
  • Farrokh Razavinia

    (Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 5375171379, Iran
    These authors contributed equally to this work.)

  • Ghorbanali Haghighatdoost

    (Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 5375171379, Iran
    These authors contributed equally to this work.)

Abstract

This is a noticeably short biography and introductory paper on multiplier Hopf algebras. It delves into questions regarding the significance of this abstract construction and the motivation behind its creation. It also concerns quantum linear groups, especially the coordinate ring of M q ( n ) and the observation that K [ M q ( n )] is a quadratic algebra, and can be equipped with a multiplier Hopf ∗-algebra structure in the sense of quantum permutation groups developed byWang 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 field of graph theory, thereby establishing connections between them! This survey review paper is dedicated to the 78th birthday anniversary of Professor Alfons Van Daele.

Suggested Citation

  • Farrokh Razavinia & Ghorbanali Haghighatdoost, 2023. "From Quantum Automorphism of (Directed) Graphs to the Associated Multiplier Hopf Algebras," Mathematics, MDPI, vol. 12(1), pages 1-38, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2023:i:1:p:128-:d:1310802
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