Salvato in:
| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2302.08027 |
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Sommario:
- A kind of combinatorial map, called arrow presentation, is proposed to encode the data of the oriented closed polyhedral complexes $Σ$ on which the Hopf algebraic Kitaev model lives. We develop a theory of arrow presentations which underlines the role of the dual of the double $\mathcal{D}(Σ)^*$ of $Σ$ as being the Schreier coset graph of the arrow presentation, explains the ribbon structure behind curves on $\mathcal{D}(Σ)^*$ and facilitates computation of holonomy with values in the algebra of the Kitaev model. In this way, we can prove ribbon operator identities for arbitrary f.d. C$^*$-Hopf algebras and arbitrary oriented closed polyhedral maps. By means of a combinatorial notion of homotopy designed specially for ribbon curves, we can rigorously formulate ''topological invariance'' of states created by ribbon operators.