Quiver Modulations and Potentials
Quiver Modulations and Potentials
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DissertationPrüfungsdatum
16.03.2017Datum der Veröffentlichung
11.04.2017Erstgutachter
Schröer, JanZweitgutachter
Burban, IgorMetadaten
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Inhalt
We introduce DWZ (Derksen-Weyman-Zelevinsky) mutation for a special class of SPs (species with potential). Generalizing a construction of Labardini-Fragoso, we associate with each triangulated, constantly weighted orbifold an SP. For such SPs the compatibility of arc flips and DWZ mutations is established. Moreover, considering not necessarily constantly weighted, unpunctured orbifolds, we define colored triangulations and associated SPs. Finally, we investigate and answer when the Jacobian algebras of two colored triangulations with the same underlying triangulation are isomorphic and prove that these algebras are always finite-dimensional.
Schlagwörter
algebraic combinatorics, representation theory, representations of quivers, cluster algebras, Auslander-Reiten sequences
Klassifikation (DDC)
510 MathematikGeuenich, Jan: Quiver Modulations and Potentials. - Bonn, 2017. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5n-46812
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5n-46812
@phdthesis{handle:20.500.11811/7162,
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5n-46812,
author = {{Jan Geuenich}},
title = {Quiver Modulations and Potentials},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2017,
month = apr,
note = {We introduce DWZ (Derksen-Weyman-Zelevinsky) mutation for a special class of SPs (species with potential). Generalizing a construction of Labardini-Fragoso, we associate with each triangulated, constantly weighted orbifold an SP. For such SPs the compatibility of arc flips and DWZ mutations is established. Moreover, considering not necessarily constantly weighted, unpunctured orbifolds, we define colored triangulations and associated SPs. Finally, we investigate and answer when the Jacobian algebras of two colored triangulations with the same underlying triangulation are isomorphic and prove that these algebras are always finite-dimensional.},
url = {https://hdl.handle.net/20.500.11811/7162}
}
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5n-46812,
author = {{Jan Geuenich}},
title = {Quiver Modulations and Potentials},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2017,
month = apr,
note = {We introduce DWZ (Derksen-Weyman-Zelevinsky) mutation for a special class of SPs (species with potential). Generalizing a construction of Labardini-Fragoso, we associate with each triangulated, constantly weighted orbifold an SP. For such SPs the compatibility of arc flips and DWZ mutations is established. Moreover, considering not necessarily constantly weighted, unpunctured orbifolds, we define colored triangulations and associated SPs. Finally, we investigate and answer when the Jacobian algebras of two colored triangulations with the same underlying triangulation are isomorphic and prove that these algebras are always finite-dimensional.},
url = {https://hdl.handle.net/20.500.11811/7162}
}
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