GIT-equivalence and semi-stable subcategories of quiver representations
In this paper, we answer the question of when the subcategory of semi-stable representations is the same for two rational vectors for an acyclic quiver. This question has been previously answered by Ingalls, Paquette, and Thomas in the tame case in [14]. Here we take a more invariant theoretic appro...
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| Published in | Journal of pure and applied algebra Vol. 223; no. 8; pp. 3499 - 3514 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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Elsevier B.V
01.08.2019
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| Abstract | In this paper, we answer the question of when the subcategory of semi-stable representations is the same for two rational vectors for an acyclic quiver. This question has been previously answered by Ingalls, Paquette, and Thomas in the tame case in [14]. Here we take a more invariant theoretic approach, to answer this question in general. We recover the known result in the tame case. |
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| AbstractList | In this paper, we answer the question of when the subcategory of semi-stable representations is the same for two rational vectors for an acyclic quiver. This question has been previously answered by Ingalls, Paquette, and Thomas in the tame case in [14]. Here we take a more invariant theoretic approach, to answer this question in general. We recover the known result in the tame case. |
| Author | Chindris, Calin Granger, Valerie |
| Author_xml | – sequence: 1 givenname: Calin surname: Chindris fullname: Chindris, Calin email: chindrisc@missouri.edu organization: University of Missouri-Columbia, Mathematics Department, Columbia, MO, USA – sequence: 2 givenname: Valerie surname: Granger fullname: Granger, Valerie email: vrhmq7@mail.missouri.edu, vgranger@coker.edu organization: University of Missouri-Columbia, Mathematics Department, Columbia, MO, USA |
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| Cites_doi | 10.1112/plms/pdv002 10.1016/0021-8693(76)90184-8 10.1007/BF02698859 10.1112/S0010437X09004023 10.1112/S0010437X09004151 10.1016/S0022-4049(01)00167-0 10.1142/S0218196712500646 10.5802/aif.2636 10.1016/j.jpaa.2008.06.005 10.1112/plms/s3-65.1.46 10.1307/mmj/1163789912 10.1093/qmath/45.4.515 10.1006/aima.2001.1986 10.1023/A:1005275524522 |
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| Keywords | 13A50 GIT-cones Tame quivers Schur roots Semi-stable quiver representations 16G20 |
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| References | Ressayre (br0210) 2000; 81 Keicher (br0170) 2012; 22 Berchtold, Hausen (br0030) 2006; 54 Derksen, Weyman (br0090) 2011; 61 Brady (br0040) 2001; 161 Ringel (br0220) 1976; 41 Schofield (br0230) 1992; 65 Crawley-Boevey (br0080) Dolgachev, Hu (br0100) 1998 King (br0180) 1994; 45 Simson, Skowroński (br0240) 2007; vol. 71 Chindris (br0060) 2008 Ingalls, Thomas (br0150) 2009; 145 Laza (br0200) 2013; vol. 25 Crawley-Boevey, Geiss (br0070) 2002 Ingalls, Paquette, Thomas (br0140) 2015; 110 Assem, Simson, Skowroński (br0020) 2006; vol. 65 Granger (br0110) 2016 Igusa, Orr, Todorov, Weyman (br0130) 2009; 145 Hille, de la Peña (br0120) 2002; 172 Kac (br0160) 1983; vol. 996 Brady, Watt (br0050) 2002; vol. 94 Arzhantsev, Hausen (br0010) 2009; 213 Crawley-Boevey (10.1016/j.jpaa.2018.11.014_br0070) 2002 Granger (10.1016/j.jpaa.2018.11.014_br0110) 2016 Ringel (10.1016/j.jpaa.2018.11.014_br0220) 1976; 41 Derksen (10.1016/j.jpaa.2018.11.014_br0090) 2011; 61 Ingalls (10.1016/j.jpaa.2018.11.014_br0150) 2009; 145 Hille (10.1016/j.jpaa.2018.11.014_br0120) 2002; 172 Brady (10.1016/j.jpaa.2018.11.014_br0040) 2001; 161 Assem (10.1016/j.jpaa.2018.11.014_br0020) 2006; vol. 65 Brady (10.1016/j.jpaa.2018.11.014_br0050) 2002; vol. 94 Simson (10.1016/j.jpaa.2018.11.014_br0240) 2007; vol. 71 Ressayre (10.1016/j.jpaa.2018.11.014_br0210) 2000; 81 Dolgachev (10.1016/j.jpaa.2018.11.014_br0100) 1998 Igusa (10.1016/j.jpaa.2018.11.014_br0130) 2009; 145 Berchtold (10.1016/j.jpaa.2018.11.014_br0030) 2006; 54 Ingalls (10.1016/j.jpaa.2018.11.014_br0140) 2015; 110 Keicher (10.1016/j.jpaa.2018.11.014_br0170) 2012; 22 King (10.1016/j.jpaa.2018.11.014_br0180) 1994; 45 Laza (10.1016/j.jpaa.2018.11.014_br0200) 2013; vol. 25 Chindris (10.1016/j.jpaa.2018.11.014_br0060) Kac (10.1016/j.jpaa.2018.11.014_br0160) 1983; vol. 996 Schofield (10.1016/j.jpaa.2018.11.014_br0230) 1992; 65 Arzhantsev (10.1016/j.jpaa.2018.11.014_br0010) 2009; 213 Crawley-Boevey (10.1016/j.jpaa.2018.11.014_br0080) |
| References_xml | – volume: 110 start-page: 805 year: 2015 end-page: 840 ident: br0140 article-title: Semi-stable subcategories for Euclidean quivers publication-title: Proc. Lond. Math. Soc. (3) contributor: fullname: Thomas – volume: 61 start-page: 1061 year: 2011 end-page: 1131 ident: br0090 article-title: The combinatorics of quiver representations publication-title: Ann. Inst. Fourier (Grenoble) contributor: fullname: Weyman – volume: 145 start-page: 1533 year: 2009 end-page: 1562 ident: br0150 article-title: Noncrossing partitions and representations of quivers publication-title: Compos. Math. contributor: fullname: Thomas – volume: 45 start-page: 515 year: 1994 end-page: 530 ident: br0180 article-title: Moduli of representations of finite-dimensional algebras publication-title: Q. J. Math. Oxf. Ser. (2) contributor: fullname: King – volume: 172 start-page: 205 year: 2002 end-page: 224 ident: br0120 article-title: Stable representations of quivers publication-title: J. Pure Appl. Algebra contributor: fullname: de la Peña – volume: vol. 65 year: 2006 ident: br0020 article-title: Elements of the Representation Theory of Associative Algebras, vol. 1: Techniques of Representation Theory publication-title: Lond. Math. Soc. Stud. Texts contributor: fullname: Skowroński – volume: vol. 94 start-page: 225 year: 2002 end-page: 250 ident: br0050 article-title: 's for Artin groups of finite type publication-title: Proceedings of the Conference on Geometric and Combinatorial Group Theory, Part I contributor: fullname: Watt – volume: 213 start-page: 154 year: 2009 end-page: 172 ident: br0010 article-title: Geometric invariant theory via Cox rings publication-title: J. Pure Appl. Algebra contributor: fullname: Hausen – volume: 145 start-page: 1001 year: 2009 end-page: 1034 ident: br0130 article-title: Cluster complexes via semi-invariants publication-title: Compos. Math. contributor: fullname: Weyman – volume: 161 start-page: 20 year: 2001 end-page: 40 ident: br0040 article-title: A partial order on the symmetric group and new publication-title: Adv. Math. contributor: fullname: Brady – volume: vol. 996 start-page: 74 year: 1983 end-page: 108 ident: br0160 article-title: Root systems, representations of quivers and invariant theory publication-title: Invariant Theory contributor: fullname: Kac – volume: 54 start-page: 483 year: 2006 end-page: 516 ident: br0030 article-title: GIT-equivalence beyond the ample cone publication-title: Mich. Math. J. contributor: fullname: Hausen – year: 2016 ident: br0110 article-title: GIT-Equivalence and Semi-stable Subcategories of Quiver Representations contributor: fullname: Granger – ident: br0080 article-title: Lectures on representations of quivers contributor: fullname: Crawley-Boevey – start-page: 5 year: 1998 end-page: 56 ident: br0100 article-title: Variation of geometric invariant theory quotients. With an appendix by Nicolas Ressayre publication-title: Inst. Hautes Études Sci. Publ. Math. contributor: fullname: Hu – volume: 41 start-page: 269 year: 1976 end-page: 302 ident: br0220 article-title: Representations of publication-title: J. Algebra contributor: fullname: Ringel – volume: vol. 25 start-page: 259 year: 2013 end-page: 297 ident: br0200 article-title: GIT and moduli with a twist publication-title: Handbook of Moduli, vol. II contributor: fullname: Laza – start-page: 40 year: 2002 end-page: 48 ident: br0070 article-title: Horn's problem and semi-stability for quiver representations publication-title: Representations of Algebra, vols. I, II contributor: fullname: Geiss – volume: 81 start-page: 295 year: 2000 end-page: 324 ident: br0210 article-title: The GIT-equivalence for publication-title: Geom. Dedic. contributor: fullname: Ressayre – volume: 22 year: 2012 ident: br0170 article-title: Computing the GIT-fan publication-title: Int. J. Algebra Comput. contributor: fullname: Keicher – volume: vol. 71 year: 2007 ident: br0240 article-title: Elements of the Representation Theory of Associative Algebras, vol. 2: Tubes and Concealed Algebras of Euclidean Type publication-title: Lond. Math. Soc. Stud. Texts contributor: fullname: Skowroński – volume: 65 start-page: 46 year: 1992 end-page: 64 ident: br0230 article-title: General representations of quivers publication-title: Proc. Lond. Math. Soc. (3) contributor: fullname: Schofield – year: 2008 ident: br0060 article-title: On GIT-fans for quivers contributor: fullname: Chindris – volume: vol. 25 start-page: 259 year: 2013 ident: 10.1016/j.jpaa.2018.11.014_br0200 article-title: GIT and moduli with a twist contributor: fullname: Laza – volume: 110 start-page: 805 issue: 4 year: 2015 ident: 10.1016/j.jpaa.2018.11.014_br0140 article-title: Semi-stable subcategories for Euclidean quivers publication-title: Proc. Lond. Math. Soc. (3) doi: 10.1112/plms/pdv002 contributor: fullname: Ingalls – volume: 41 start-page: 269 issue: 2 year: 1976 ident: 10.1016/j.jpaa.2018.11.014_br0220 article-title: Representations of K-species and bimodules publication-title: J. Algebra doi: 10.1016/0021-8693(76)90184-8 contributor: fullname: Ringel – start-page: 5 issue: 87 year: 1998 ident: 10.1016/j.jpaa.2018.11.014_br0100 article-title: Variation of geometric invariant theory quotients. With an appendix by Nicolas Ressayre publication-title: Inst. Hautes Études Sci. Publ. Math. doi: 10.1007/BF02698859 contributor: fullname: Dolgachev – volume: 145 start-page: 1533 issue: 6 year: 2009 ident: 10.1016/j.jpaa.2018.11.014_br0150 article-title: Noncrossing partitions and representations of quivers publication-title: Compos. Math. doi: 10.1112/S0010437X09004023 contributor: fullname: Ingalls – volume: vol. 94 start-page: 225 year: 2002 ident: 10.1016/j.jpaa.2018.11.014_br0050 article-title: K(π,1)'s for Artin groups of finite type contributor: fullname: Brady – volume: 145 start-page: 1001 issue: 4 year: 2009 ident: 10.1016/j.jpaa.2018.11.014_br0130 article-title: Cluster complexes via semi-invariants publication-title: Compos. Math. doi: 10.1112/S0010437X09004151 contributor: fullname: Igusa – volume: 172 start-page: 205 issue: 2–3 year: 2002 ident: 10.1016/j.jpaa.2018.11.014_br0120 article-title: Stable representations of quivers publication-title: J. Pure Appl. Algebra doi: 10.1016/S0022-4049(01)00167-0 contributor: fullname: Hille – volume: 22 issue: 7 year: 2012 ident: 10.1016/j.jpaa.2018.11.014_br0170 article-title: Computing the GIT-fan publication-title: Int. J. Algebra Comput. doi: 10.1142/S0218196712500646 contributor: fullname: Keicher – volume: 61 start-page: 1061 issue: 3 year: 2011 ident: 10.1016/j.jpaa.2018.11.014_br0090 article-title: The combinatorics of quiver representations publication-title: Ann. Inst. Fourier (Grenoble) doi: 10.5802/aif.2636 contributor: fullname: Derksen – start-page: 40 year: 2002 ident: 10.1016/j.jpaa.2018.11.014_br0070 article-title: Horn's problem and semi-stability for quiver representations contributor: fullname: Crawley-Boevey – volume: 213 start-page: 154 issue: 1 year: 2009 ident: 10.1016/j.jpaa.2018.11.014_br0010 article-title: Geometric invariant theory via Cox rings publication-title: J. Pure Appl. Algebra doi: 10.1016/j.jpaa.2008.06.005 contributor: fullname: Arzhantsev – volume: 65 start-page: 46 issue: 1 year: 1992 ident: 10.1016/j.jpaa.2018.11.014_br0230 article-title: General representations of quivers publication-title: Proc. Lond. Math. Soc. (3) doi: 10.1112/plms/s3-65.1.46 contributor: fullname: Schofield – volume: 54 start-page: 483 issue: 3 year: 2006 ident: 10.1016/j.jpaa.2018.11.014_br0030 article-title: GIT-equivalence beyond the ample cone publication-title: Mich. Math. J. doi: 10.1307/mmj/1163789912 contributor: fullname: Berchtold – ident: 10.1016/j.jpaa.2018.11.014_br0080 contributor: fullname: Crawley-Boevey – year: 2016 ident: 10.1016/j.jpaa.2018.11.014_br0110 contributor: fullname: Granger – volume: vol. 996 start-page: 74 year: 1983 ident: 10.1016/j.jpaa.2018.11.014_br0160 article-title: Root systems, representations of quivers and invariant theory contributor: fullname: Kac – ident: 10.1016/j.jpaa.2018.11.014_br0060 contributor: fullname: Chindris – volume: vol. 71 year: 2007 ident: 10.1016/j.jpaa.2018.11.014_br0240 article-title: Elements of the Representation Theory of Associative Algebras, vol. 2: Tubes and Concealed Algebras of Euclidean Type contributor: fullname: Simson – volume: 45 start-page: 515 issue: 180 year: 1994 ident: 10.1016/j.jpaa.2018.11.014_br0180 article-title: Moduli of representations of finite-dimensional algebras publication-title: Q. J. Math. Oxf. Ser. (2) doi: 10.1093/qmath/45.4.515 contributor: fullname: King – volume: 161 start-page: 20 issue: 1 year: 2001 ident: 10.1016/j.jpaa.2018.11.014_br0040 article-title: A partial order on the symmetric group and new K(π,1)'s for the braid groups publication-title: Adv. Math. doi: 10.1006/aima.2001.1986 contributor: fullname: Brady – volume: 81 start-page: 295 issue: 1–3 year: 2000 ident: 10.1016/j.jpaa.2018.11.014_br0210 article-title: The GIT-equivalence for G-line bundles publication-title: Geom. Dedic. doi: 10.1023/A:1005275524522 contributor: fullname: Ressayre – volume: vol. 65 year: 2006 ident: 10.1016/j.jpaa.2018.11.014_br0020 article-title: Elements of the Representation Theory of Associative Algebras, vol. 1: Techniques of Representation Theory contributor: fullname: Assem |
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| Title | GIT-equivalence and semi-stable subcategories of quiver representations |
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