Classification of Quantum Graphs on $M_2$ and their Quantum Automorphism Groups

Autor:	Junichiro Matsuda
Jazyk:	angličtina
Rok vydání:	2021
Předmět:	Mathematics::Operator Algebras FOS: Mathematics Mathematics - Operator Algebras Statistical and Nonlinear Physics Operator Algebras (math.OA) Mathematical Physics
Popis:	Motivated by string diagrammatic approach to undirected tracial quantum graphs by Musto, Reutter, Verdon (2018), in the former part of this paper we diagrammatically formulate directed nontracial quantum graphs by Brannan, Chirvasitu, Eifler, Harris, Paulsen, Su, Wasilewski (2019). In the latter part, we supply a concrete classification of undirected reflexive quantum graphs on $M_2$ and their quantum automorphism groups in both tracial and nontracial settings. We also obtain quantum isomorphisms between tracial quantum graphs on $M_2$ and certain classical graphs, which reproves the monoidal equivalences between $SO(3)$ and $S_4^+$, and $O(2)$ and $H_2^+$. 44 pages; typos corrected
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e0d8ed74a2b4b2e118e7fb041b76dbde http://arxiv.org/abs/2110.09085 Zobrazit plný text záznamu