Solution group representations as quantum symmetries of graphs

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Solution group representations as quantum symmetries of graphs. / Roberson, David E.; Schmidt, Simon.

I: Journal of the London Mathematical Society, Bind 106, Nr. 4, 2022, s. 3379-3410.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Roberson, DE & Schmidt, S 2022, 'Solution group representations as quantum symmetries of graphs', Journal of the London Mathematical Society, bind 106, nr. 4, s. 3379-3410. https://doi.org/10.1112/jlms.12664

APA

Roberson, D. E., & Schmidt, S. (2022). Solution group representations as quantum symmetries of graphs. Journal of the London Mathematical Society, 106(4), 3379-3410. https://doi.org/10.1112/jlms.12664

Vancouver

Roberson DE, Schmidt S. Solution group representations as quantum symmetries of graphs. Journal of the London Mathematical Society. 2022;106(4):3379-3410. https://doi.org/10.1112/jlms.12664

Author

Roberson, David E. ; Schmidt, Simon. / Solution group representations as quantum symmetries of graphs. I: Journal of the London Mathematical Society. 2022 ; Bind 106, Nr. 4. s. 3379-3410.

Bibtex

@article{dab271b88c6e48ba8facdece14d31328,
title = "Solution group representations as quantum symmetries of graphs",
abstract = "In 2019, Aterias et al. constructed pairs of quantum isomorphic, non-isomorphic graphs from linear constraint systems. This article deals with quantum automorphisms and quantum isomorphisms of colored versions of those graphs. We show that the quantum automorphism group of such a colored graph is the dual of the homogeneous solution group of the underlying linear constraint system. Given a vertex- and edge-colored graph with certain properties, we construct an uncolored graph that has the same quantum automorphism group as the colored graph we started with. Using those results, we obtain the first-known example of a graph that has quantum symmetry and finite quantum automorphism group. Furthermore, we construct a pair of quantum isomorphic, non-isomorphic graphs that both have no quantum symmetry.",
author = "Roberson, {David E.} and Simon Schmidt",
year = "2022",
doi = "10.1112/jlms.12664",
language = "English",
volume = "106",
pages = "3379--3410",
journal = "Journal of the London Mathematical Society",
issn = "0024-6107",
publisher = "Oxford University Press",
number = "4",

}

RIS

TY - JOUR

T1 - Solution group representations as quantum symmetries of graphs

AU - Roberson, David E.

AU - Schmidt, Simon

PY - 2022

Y1 - 2022

N2 - In 2019, Aterias et al. constructed pairs of quantum isomorphic, non-isomorphic graphs from linear constraint systems. This article deals with quantum automorphisms and quantum isomorphisms of colored versions of those graphs. We show that the quantum automorphism group of such a colored graph is the dual of the homogeneous solution group of the underlying linear constraint system. Given a vertex- and edge-colored graph with certain properties, we construct an uncolored graph that has the same quantum automorphism group as the colored graph we started with. Using those results, we obtain the first-known example of a graph that has quantum symmetry and finite quantum automorphism group. Furthermore, we construct a pair of quantum isomorphic, non-isomorphic graphs that both have no quantum symmetry.

AB - In 2019, Aterias et al. constructed pairs of quantum isomorphic, non-isomorphic graphs from linear constraint systems. This article deals with quantum automorphisms and quantum isomorphisms of colored versions of those graphs. We show that the quantum automorphism group of such a colored graph is the dual of the homogeneous solution group of the underlying linear constraint system. Given a vertex- and edge-colored graph with certain properties, we construct an uncolored graph that has the same quantum automorphism group as the colored graph we started with. Using those results, we obtain the first-known example of a graph that has quantum symmetry and finite quantum automorphism group. Furthermore, we construct a pair of quantum isomorphic, non-isomorphic graphs that both have no quantum symmetry.

U2 - 10.1112/jlms.12664

DO - 10.1112/jlms.12664

M3 - Journal article

VL - 106

SP - 3379

EP - 3410

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

SN - 0024-6107

IS - 4

ER -

ID: 313480327