Combinatorics and Graph Theory

    

Quantum Partial Automorphisms of Finite Graphs

Authors: Teo Banica

The partial automorphisms of a graph $X$ having $N$ vertices are the bijections $\sigma:I\to J$ with $I,J\subset\{1,\ldots,N\}$ which leave invariant the edges. These bijections form a semigroup $\widetilde{G}(X)$, which contains the automorphism group $G(X)$. We discuss here the quantum analogue of this construction, with a definition and basic theory for the quantum semigroup of quantum partial automorphisms $\widetilde{G}^+(X)$, which contains both $G(X)$, and the quantum automorphism group $G^+(X)$. We comment as well on the case $N=\infty$, which is of particular interest, due to the fact that $\widetilde{G}^+(X)$ is well-defined, while its subgroup $G^+(X)$, not necessarily, at least with the currently known methods.

Comments: 28 Pages.

Download: PDF

Submission history

[v1] 2021-05-20 08:17:09

Unique-IP document downloads: 369 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus