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dc.contributor.authorCowtan, A
dc.contributor.authorMajid, S
dc.date.accessioned2023-11-28T15:21:03Z
dc.date.available2023-11-28T15:21:03Z
dc.date.issued2022-08-12
dc.identifier.urihttps://qmro.qmul.ac.uk/xmlui/handle/123456789/92346
dc.description.abstractWe provide a systematic treatment of boundaries based on subgroups K ⊆ G for the Kitaev quantum double D(G) model in the bulk. The boundary sites are representations of a -subalgebra Ξ ⊆ D(G) and we explicate its structure as a quasi-Hopf -algebra dependent on a choice of transversal R. We provide decomposition formulae for irreducible representations of D(G) pulled back to Ξ. As an application of our treatment, we study patches with boundaries based on K = G horizontally and K = {e} vertically and show how these could be used in a quantum computer using the technique of lattice surgery. More abstractly, we also provide explicitly the monoidal equivalence of the category of Ξ-modules and the category of G-graded K-bimodules and use this to prove that different choices of R are related by Drinfeld cochain twists. Examples include Sn−1 ⊂ Sn and an example related to the octonions where Ξ is also a Hopf quasigroup.en_US
dc.publisherAIP Publishingen_US
dc.rightsAll article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
dc.rightsAttribution 3.0 United States*
dc.rights.urihttp://creativecommons.org/licenses/by/3.0/us/*
dc.subjectquant-phen_US
dc.subjectquant-phen_US
dc.subjectmath-phen_US
dc.subjectmath.MPen_US
dc.subjectmath.QAen_US
dc.titleAlgebraic Aspects of Boundaries in the Kitaev Quantum Double Modelen_US
dc.rights.holder© 2023 Author(s).
pubs.author-urlhttp://arxiv.org/abs/2208.06317v1en_US
pubs.notesNot knownen_US
rioxxterms.funderDefault funderen_US
rioxxterms.identifier.projectDefault projecten_US


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All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Except where otherwise noted, this item's license is described as All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).