From Quantum Automorphism of (Directed) Graphs to the Associated Multiplier Hopf Algebras
-
Published:2023-12-30
Issue:1
Volume:12
Page:128
-
ISSN:2227-7390
-
Container-title:Mathematics
-
language:en
-
Short-container-title:Mathematics
Author:
Razavinia Farrokh1ORCID,
Haghighatdoost Ghorbanali1ORCID
Affiliation:
1. Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 5375171379, Iran
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 Mq(n) and the observation that K [Mq(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.
Funder
Azarbaijan Shahid Madani University
Department of Mathematics of the Azarbaijan Shahid Madani University
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference46 articles.
1. A new approach to the Tomita-Takesaki theory of generalized Hilbert algebras;J. Funct. Anal.,1974
2. Discrete quantum groups;J. Algebra,1996
3. Multiplier Hopf algebras;Trans. Am. Math. Soc.,1994
4. Van Daele, A. (2023). Algebraic quantum groups and duality I. arXiv.
5. Van Daele, A. (2023). Algebraic quantum groups and duality II. Multiplier Hopf ∗-algebras with positive integrals. arXiv.