Affiliation:
1. Department of Mathematics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan
Abstract
Motivated by the string diagrammatic approach to undirected tracial quantum graphs by Musto et al. [J. Math. Phys. 59(8), 081706 (2018)], in the former part of this paper, we diagrammatically formulate directed nontracial quantum graphs by Brannan et al. [Commun. Math. Phys. 375(3), 1777 (2019)]. In the latter part, we supply a concrete classification of undirected reflexive quantum graphs on M2and their quantum automorphism groups in both tracial and nontracial settings. We also obtain quantum isomorphisms between tracial quantum graphs on M2and certain classical graphs, which reproves the monoidal equivalences between SO(3) and [Formula: see text] and O(2) and [Formula: see text].
Funder
JST, The Establishment of University Fellowships Toward the Creation of Science Technology Innovation
Subject
Mathematical Physics,Statistical and Nonlinear Physics
Cited by
1 articles.
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1. Some examples of quantum graphs;Letters in Mathematical Physics;2022-11-25