REPETITIVE CLUSTER-TILTED ALGEBRAS
Let H be a finite-dimensional hereditary algebra over an algebraically closed field k and CFm be the repetitive cluster category of H with m ≥ 1. We investigate the properties of cluster tilting objects in CFm and the structure of repetitive clustertilted algebras. Moreover, we generalize Theorem 4....
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| Published in | Acta mathematica scientia Vol. 32; no. 4; pp. 1449 - 1454 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
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Elsevier Ltd
01.07.2012
School of Mathematics, Shandong University, Jinan 250100, China%Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China |
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| Online Access | Get full text |
| ISSN | 0252-9602 1572-9087 |
| DOI | 10.1016/S0252-9602(12)60114-3 |
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| Abstract | Let H be a finite-dimensional hereditary algebra over an algebraically closed field k and CFm be the repetitive cluster category of H with m ≥ 1. We investigate the properties of cluster tilting objects in CFm and the structure of repetitive clustertilted algebras. Moreover, we generalize Theorem 4.2 in [12] （Buan A, Marsh R, Reiten I. Cluster-tilted algebra, Trans. Amer. Math. Soc. 359（1）（2007）, 323-332.） to the situation of C Fm, and prove that the tilting graph KCFm of CFm is connected. |
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| AbstractList | O411.1; Let H be a finite-dimensional hereditary algebra over an algebraically closed field k and CFm be the repetitive cluster category of H with m ≥ 1.We investigate the properties of cluster tilting objects in CFm and the structure of repetitive clustertilted algebras.Moreover,we generalize Theorem 4.2 in [12](Buan A,Marsh R,Reiten I.Cluster-tilted algebra,Trans.Amer.Math.Soc.,359(1)(2007),323-332.) to the situation of CFm,and prove that the tilting graph KCFm of CFm is connected. Let H be a finite-dimensional hereditary algebra over an algebraically closed field k and CFm be the repetitive cluster category of H with m ≥ 1. We investigate the properties of cluster tilting objects in CFm and the structure of repetitive clustertilted algebras. Moreover, we generalize Theorem 4.2 in [12] （Buan A, Marsh R, Reiten I. Cluster-tilted algebra, Trans. Amer. Math. Soc. 359（1）（2007）, 323-332.） to the situation of C Fm, and prove that the tilting graph KCFm of CFm is connected. Let H be a finite-dimensional hereditary algebra over an algebraically closed field k and CFm be the repetitive cluster category of H with m ≥ 1. We investigate the properties of cluster tilting objects in CFm and the structure of repetitive cluster-tilted algebras. Moreover, we generalize Theorem 4.2 in [12] (Buan A, Marsh R, Reiten I. Cluster-tilted algebra, Trans. Amer. Math. Soc., 359(1)(2007), 323-332.) to the situation of CFm, and prove that the tilting graph KCFm of CFm is connected. |
| Author | 张顺华 张跃辉 |
| AuthorAffiliation | School of Mathematics, Shandong University, Jinan 250100, China Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China |
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| Cites_doi | 10.1016/j.aim.2006.06.002 10.1016/j.aim.2005.06.003 10.1016/j.jalgebra.2004.11.007 10.1090/S0894-0347-01-00385-X 10.1080/00927872.2010.489082 10.1016/j.aim.2006.07.013 10.1016/j.ansens.2006.09.003 10.1007/s00222-008-0111-4 10.1090/S0002-9947-06-03879-7 10.1007/s00209-007-0165-9 10.4171/dm/199 10.1016/j.aim.2006.06.003 |
| ClassificationCodes | O411.1 |
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| Copyright | 2012 Wuhan Institute of Physics and Mathematics Copyright © Wanfang Data Co. Ltd. All Rights Reserved. |
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| Keywords | repetitive cluster-tilted algebra cluster tilting object 16G20 repetitive cluster category 16G70 |
| Language | English |
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| Notes | repetitive cluster category; cluster tilting object; repetitive cluster-tiltedalgebra Let H be a finite-dimensional hereditary algebra over an algebraically closed field k and CFm be the repetitive cluster category of H with m ≥ 1. We investigate the properties of cluster tilting objects in CFm and the structure of repetitive clustertilted algebras. Moreover, we generalize Theorem 4.2 in [12] （Buan A, Marsh R, Reiten I. Cluster-tilted algebra, Trans. Amer. Math. Soc. 359（1）（2007）, 323-332.） to the situation of C Fm, and prove that the tilting graph KCFm of CFm is connected. 42-1227/O |
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| Snippet | Let H be a finite-dimensional hereditary algebra over an algebraically closed field k and CFm be the repetitive cluster category of H with m ≥ 1. We... O411.1; Let H be a finite-dimensional hereditary algebra over an algebraically closed field k and CFm be the repetitive cluster category of H with m ≥ 1.We... |
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| SubjectTerms | 16G20 16G70 CFM cluster tilting object repetitive cluster category repetitive cluster-tilted algebra 代数簇 代数闭域 倾斜代数 归纳定理 有限维 遗传代数 集群 |
| Title | REPETITIVE CLUSTER-TILTED ALGEBRAS |
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