Complete Intersection Quiver Settings with One Dimensional Vertices
Abstract We describe the class of quiver settings with one dimensional vertices whose semi-simple representations are parametrized by a complete intersection variety. We show that these quivers can be reduced to a one vertex quiver with some combinatorial reduction steps. We introduce the notion of...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Joó, Dániel [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2012 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media B.V. 2012 |
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| Übergeordnetes Werk: |
Enthalten in: Algebras and representation theory - Springer Netherlands, 1998, 16(2012), 4 vom: 26. Mai, Seite 1109-1133 |
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| Übergeordnetes Werk: |
volume:16 ; year:2012 ; number:4 ; day:26 ; month:05 ; pages:1109-1133 |
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| DOI / URN: |
10.1007/s10468-012-9348-0 |
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OLC2036438601 |
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| 520 | |a Abstract We describe the class of quiver settings with one dimensional vertices whose semi-simple representations are parametrized by a complete intersection variety. We show that these quivers can be reduced to a one vertex quiver with some combinatorial reduction steps. We introduce the notion of descendants which is similar to graph theoretic minors, and show that the class in question can be characterized as the quivers that do not have two specific forbidden descendants. We also prove that the class of coregular quiver settings with arbitrary dimension vector, which has been understood earlier via reduction steps, can also be described as the ones that do not contain a certain forbidden descendant. | ||
| 650 | 4 | |a Quiver settings | |
| 650 | 4 | |a Complete intersections | |
| 650 | 4 | |a Representation theory | |
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10.1007/s10468-012-9348-0 doi (DE-627)OLC2036438601 (DE-He213)s10468-012-9348-0-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn 31.23$jIdeale$jRinge$jModuln$jAlgebren$XMathematik bkl 31.21$jGruppentheorie bkl Joó, Dániel verfasserin aut Complete Intersection Quiver Settings with One Dimensional Vertices 2012 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media B.V. 2012 Abstract We describe the class of quiver settings with one dimensional vertices whose semi-simple representations are parametrized by a complete intersection variety. We show that these quivers can be reduced to a one vertex quiver with some combinatorial reduction steps. We introduce the notion of descendants which is similar to graph theoretic minors, and show that the class in question can be characterized as the quivers that do not have two specific forbidden descendants. We also prove that the class of coregular quiver settings with arbitrary dimension vector, which has been understood earlier via reduction steps, can also be described as the ones that do not contain a certain forbidden descendant. Quiver settings Complete intersections Representation theory Enthalten in Algebras and representation theory Springer Netherlands, 1998 16(2012), 4 vom: 26. Mai, Seite 1109-1133 (DE-627)254285066 (DE-600)1463085-0 (DE-576)081894716 1386-923X nnns volume:16 year:2012 number:4 day:26 month:05 pages:1109-1133 https://doi.org/10.1007/s10468-012-9348-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_2088 GBV_ILN_4310 31.23$jIdeale$jRinge$jModuln$jAlgebren$XMathematik VZ 106418971 (DE-625)106418971 31.21$jGruppentheorie VZ 106408445 (DE-625)106408445 AR 16 2012 4 26 05 1109-1133 |
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Complete Intersection Quiver Settings with One Dimensional Vertices |
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Abstract We describe the class of quiver settings with one dimensional vertices whose semi-simple representations are parametrized by a complete intersection variety. We show that these quivers can be reduced to a one vertex quiver with some combinatorial reduction steps. We introduce the notion of descendants which is similar to graph theoretic minors, and show that the class in question can be characterized as the quivers that do not have two specific forbidden descendants. We also prove that the class of coregular quiver settings with arbitrary dimension vector, which has been understood earlier via reduction steps, can also be described as the ones that do not contain a certain forbidden descendant. © Springer Science+Business Media B.V. 2012 |
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Abstract We describe the class of quiver settings with one dimensional vertices whose semi-simple representations are parametrized by a complete intersection variety. We show that these quivers can be reduced to a one vertex quiver with some combinatorial reduction steps. We introduce the notion of descendants which is similar to graph theoretic minors, and show that the class in question can be characterized as the quivers that do not have two specific forbidden descendants. We also prove that the class of coregular quiver settings with arbitrary dimension vector, which has been understood earlier via reduction steps, can also be described as the ones that do not contain a certain forbidden descendant. © Springer Science+Business Media B.V. 2012 |
| abstract_unstemmed |
Abstract We describe the class of quiver settings with one dimensional vertices whose semi-simple representations are parametrized by a complete intersection variety. We show that these quivers can be reduced to a one vertex quiver with some combinatorial reduction steps. We introduce the notion of descendants which is similar to graph theoretic minors, and show that the class in question can be characterized as the quivers that do not have two specific forbidden descendants. We also prove that the class of coregular quiver settings with arbitrary dimension vector, which has been understood earlier via reduction steps, can also be described as the ones that do not contain a certain forbidden descendant. © Springer Science+Business Media B.V. 2012 |
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| title_short |
Complete Intersection Quiver Settings with One Dimensional Vertices |
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https://doi.org/10.1007/s10468-012-9348-0 |
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10.1007/s10468-012-9348-0 |
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