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Continuous quivers of type A (IV) continuous mutation and geometric models of E-clusters

Daisie Rock (UGent)
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Abstract
This if the final paper in the series Continuous Quivers of Type A. In this part, we generalize existing geometric models of type A cluster structures for the new E-clusters introduced in part (III). We also introduce an isomorphism of cluster theories and a weak equivalence of cluster theories. Examples of both are given. We use these geometric models and isomorphisms of cluster theories to begin classifying continuous type A cluster theories. We also introduce a continuous generalization of mutation. This encompasses mu- tation and (infinite) sequences of mutation. Then we link continuous mutation to our earlier geometric models. Finally, we introduce the space of mutations which generalizes the exchange graph of a cluster structure, and show that paths in this space are continuous mutations.
Keywords
cluster categories, mutation, quiver representations, continuous quivers, cluster algebras, 2-CALABI-YAU CATEGORIES, ALGEBRAS

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Citation

Please use this url to cite or link to this publication:

MLA
Rock, Daisie. “Continuous Quivers of Type A (IV) Continuous Mutation and Geometric Models of E-Clusters.” ALGEBRAS AND REPRESENTATION THEORY, vol. 26, 2023, pp. 2255–88, doi:10.1007/s10468-022-10175-w.
APA
Rock, D. (2023). Continuous quivers of type A (IV) continuous mutation and geometric models of E-clusters. ALGEBRAS AND REPRESENTATION THEORY, 26, 2255–2288. https://doi.org/10.1007/s10468-022-10175-w
Chicago author-date
Rock, Daisie. 2023. “Continuous Quivers of Type A (IV) Continuous Mutation and Geometric Models of E-Clusters.” ALGEBRAS AND REPRESENTATION THEORY 26: 2255–88. https://doi.org/10.1007/s10468-022-10175-w.
Chicago author-date (all authors)
Rock, Daisie. 2023. “Continuous Quivers of Type A (IV) Continuous Mutation and Geometric Models of E-Clusters.” ALGEBRAS AND REPRESENTATION THEORY 26: 2255–2288. doi:10.1007/s10468-022-10175-w.
Vancouver
1.
Rock D. Continuous quivers of type A (IV) continuous mutation and geometric models of E-clusters. ALGEBRAS AND REPRESENTATION THEORY. 2023;26:2255–88.
IEEE
[1]
D. Rock, “Continuous quivers of type A (IV) continuous mutation and geometric models of E-clusters,” ALGEBRAS AND REPRESENTATION THEORY, vol. 26, pp. 2255–2288, 2023.
@article{8770858,
  abstract     = {{This if the final paper in the series Continuous Quivers of Type A. In this part, we generalize existing geometric models of type A cluster structures for the new E-clusters introduced in part (III). We also introduce an isomorphism of cluster theories and a weak equivalence of cluster theories. Examples of both are given. We use these geometric models and isomorphisms of cluster theories to begin classifying continuous type A cluster theories. We also introduce a continuous generalization of mutation. This encompasses mu- tation and (infinite) sequences of mutation. Then we link continuous mutation to our earlier geometric models. Finally, we introduce the space of mutations which generalizes the exchange graph of a cluster structure, and show that paths in this space are continuous mutations.}},
  author       = {{Rock, Daisie}},
  issn         = {{1386-923X}},
  journal      = {{ALGEBRAS AND REPRESENTATION THEORY}},
  keywords     = {{cluster categories,mutation,quiver representations,continuous quivers,cluster algebras,2-CALABI-YAU CATEGORIES,ALGEBRAS}},
  language     = {{eng}},
  pages        = {{2255--2288}},
  title        = {{Continuous quivers of type A (IV) continuous mutation and geometric models of E-clusters}},
  url          = {{http://doi.org/10.1007/s10468-022-10175-w}},
  volume       = {{26}},
  year         = {{2023}},
}

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