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Volumn 362, Issue 2, 2010, Pages 859-895

On cluster algebras with coefficients and 2-Calabi-Yau categories

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EID: 77349102035     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-09-04979-4     Document Type: Article
Times cited : (121)

References (42)
  • 4
    • 35448967137 scopus 로고    scopus 로고
    • Cluster-tilting theory, Trends in representation theory of algebras and related topics
    • Amer. Math. Soc., Providence, RI, MR2258039 (2008f:16031)
    • Aslak Bakke Buan and Robert Marsh, Cluster-tilting theory, Trends in representation theory of algebras and related topics, Contemp. Math., vol. 406, Amer. Math. Soc., Providence, RI, 2006, pp. 1-30. MR2258039 (2008f:16031)
    • (2006) Contemp. Math. , vol.406 , pp. 1-30
    • Buan, A.B.1    Marsh, R.2
  • 6
    • 33745809861 scopus 로고    scopus 로고
    • Tilting theory and cluster combinatorics
    • DOI 10.1016/j.aim.2005.06.003, PII S0001870805001763
    • Aslak Bakke Buan, Robert J. Marsh, Markus Reineke, Idun Reiten, and Gordana Todorov, Tilting theory and cluster combinatorics, Advances in Mathematics 204 (2) (2006), 572-618. MR2249625 (2007f:16033) (Pubitemid 44028479)
    • (2006) Advances in Mathematics , vol.204 , Issue.2 , pp. 572-618
    • Buan, A.B.1    Marsh, R.2    Reineke, M.3    Reiten, I.4    Todorov, G.5
  • 7
    • 77950655076 scopus 로고    scopus 로고
    • Clusters and seeds in acyclic cluster algebras
    • (electronic), With an appendix coauthored in addition by P. Caldero and B. Keller. MR2322734 (2008j:16044)
    • Aslak Bakke Buan, Robert J. Marsh, Idun Reiten, and Gordana Todorov, Clusters and seeds in acyclic cluster algebras, Proc. Amer. Math. Soc. 135 (2007), no. 10, 3049-3060 (electronic), With an appendix coauthored in addition by P. Caldero and B. Keller. MR2322734 (2008j:16044)
    • (2007) Proc. Amer. Math. Soc. , vol.135 , Issue.10 , pp. 3049-3060
    • Buan, A.B.1    Marsh Robert, J.2    Reiten, I.3    Todorov, G.4
  • 8
    • 12744281268 scopus 로고    scopus 로고
    • Cluster algebras. III. Upper bounds and double Bruhat cells
    • MR2110627 (2005i:16065)
    • Arkady Berenstein, Sergey Fomin, and Andrei Zelevinsky, Cluster algebras. III. Upper bounds and double Bruhat cells, Duke Math. J. 126 (2005), no. 1, 1-52. MR2110627 (2005i:16065)
    • (2005) Duke Math. J. , vol.126 , Issue.1 , pp. 1-52
    • Berenstein, A.1    Fomin, S.2    Zelevinsky, A.3
  • 9
    • 33750855116 scopus 로고    scopus 로고
    • Cluster algebras as Hall algebras of quiver representations
    • Philippe Caldero and Frédéric Chapoton, Cluster algebras as Hall algebras of quiver representations, Comment. Math. Helv. 81 (2006), no. 3, 595-616. MR2250855 (2008b:16015) (Pubitemid 44718694)
    • (2006) Commentarii Mathematici Helvetici , vol.81 , Issue.3 , pp. 595-616
    • Caldero, P.1    Chapoton, F.2
  • 10
    • 33947407721 scopus 로고    scopus 로고
    • From triangulated categories to cluster algebras. II
    • MR2316979 (2008m:16031)
    • Philippe Caldero and Bernhard Keller, From triangulated categories to cluster algebras. II, Ann. Sci. école Norm. Sup. (4) 39 (2006), no. 6, 983-1009. MR2316979 (2008m:16031)
    • (2006) Ann. Sci. école Norm. Sup. (4) , vol.39 , Issue.6 , pp. 983-1009
    • Caldero, P.1    Keller, B.2
  • 11
    • 41249083675 scopus 로고    scopus 로고
    • From triangulated categories to cluster algebras
    • MR2385670
    • Philippe Caldero and Bernhard Keller, From triangulated categories to cluster algebras, Invent. Math. 172 (2008), 169-211. MR2385670
    • (2008) Invent. Math. , vol.172 , pp. 169-211
    • Caldero, P.1    Keller, B.2
  • 13
    • 61749087162 scopus 로고    scopus 로고
    • On the combinatorics of rigid objects in 2 Calabi-yau categories
    • rnn029-17
    • Raika Dehy and Bernhard Keller, On the combinatorics of rigid objects in 2-Calabi-Yau categories, International Mathematics Research Notices 2008 (2008), rnn029-17.
    • (2008) International Mathematics Research Notices , vol.2008
    • Dehy, R.1    Keller, B.2
  • 19
    • 0036004369 scopus 로고    scopus 로고
    • Cluster algebras. I foundations
    • (electronic). MR1887642 (2003f:16050)
    • Sergey Fomin and Andrei Zelevinsky, Cluster algebras. I. Foundations, J. Amer. Math. Soc. 15 (2002), no. 2, 497-529 (electronic). MR1887642 (2003f:16050)
    • (2002) J. Amer. Math. Soc. , vol.15 , Issue.2
    • Fomin, S.1    Zelevinsky, A.2
  • 20
    • 0141457388 scopus 로고    scopus 로고
    • Cluster algebras. II. Finite type classification
    • MR2004457 (2004m:17011)
    • Cluster algebras. II. Finite type classification, Invent. Math. 154 (2003), no. 1, 63-121. MR2004457 (2004m:17011)
    • (2003) Invent. Math. , vol.154 , Issue.1
  • 21
    • 34248372052 scopus 로고    scopus 로고
    • Cluster algebras IV: Coefficients
    • R2295199 (2008d:16049)
    • Cluster algebras IV: Coefficients, Compositio Mathematica 143 (2007), 112-164. R2295199 (2008d:16049)
    • (2007) Compositio Mathematica , vol.143 , pp. 112-164
  • 22
    • 0003208834 scopus 로고
    • Representations of finite-dimensional algebras
    • Springer-Verlag, MR1239447 (94h:16001b)
    • P. Gabriel and A.V. Roiter, Representations of finite-dimensional algebras, Encyclopaedia Math. Sci., vol. 73, Springer-Verlag, 1992. MR1239447 (94h:16001b)
    • (1992) Encyclopaedia Math. Sci. , vol.73
    • Gabriel, P.1    Roiter, A.V.2
  • 24
    • 77950910187 scopus 로고    scopus 로고
    • Preprojective algebras and cluster algebras
    • Survey article to appear in the arXiv:0804.3168
    • Preprojective algebras and cluster algebras, Survey article to appear in the Proceedings of the ICRA XII, arXiv:0804.3168.
    • Proceedings of the ICRA XII
  • 25
    • 20444419032 scopus 로고    scopus 로고
    • Semicanonical bases and preprojective algebras
    • MR2144987 (2007h:17018)
    • Semicanonical bases and preprojective algebras, Ann. Sci. école Norm. Sup. (4) 38 (2005), no. 2, 193-253. MR2144987 (2007h:17018)
    • (2005) Ann. Sci. école Norm. Sup. (4) , vol.38 , Issue.2 , pp. 193-253
  • 26
    • 33746716162 scopus 로고    scopus 로고
    • Rigid modules over preprojective algebras
    • MR2242628 (2007g:16023)
    • Rigid modules over preprojective algebras, Invent.Math. 165 (2006), no. 3, 589-632. MR2242628 (2007g:16023)
    • (2006) Invent. Math. , vol.165 , Issue.3 , pp. 589-632
  • 27
    • 12744256965 scopus 로고    scopus 로고
    • Cluster algebras and Poisson geometry
    • {Dedicated to Vladimir Igorevich Arnold on the occasion of his 65th birthday}. MR2078567 (2005i:53104)
    • Michael Gekhtman, Michael Shapiro, and Alek Vainshtein, Cluster algebras and Poisson geometry, Mosc. Math. J. 3 (2003), no. 3, 899-934, 1199, {Dedicated to Vladimir Igorevich Arnold on the occasion of his 65th birthday}. MR2078567 (2005i:53104)
    • (2003) Mosc. Math. J. , vol.3 , Issue.3 , pp. 899-934
    • Gekhtman, M.1    Shapiro, M.2    Vainshtein, A.3
  • 28
    • 18144396883 scopus 로고    scopus 로고
    • Cluster algebras and Weil-Petersson forms
    • MR2130414 (2006d:53103)
    • Cluster algebras and Weil-Petersson forms, Duke Math. J. 127 (2005), no. 2, 291- 311. MR2130414 (2006d:53103)
    • (2005) Duke Math. J. , vol.127 , Issue.2 , pp. 291-311
  • 29
    • 51249178397 scopus 로고
    • On the derived category of a finite-dimensional algebra
    • MR910167 (89c:16029)
    • Dieter Happel, On the derived category of a finite-dimensional algebra, Comment. Math. Helv. 62 (1987), no. 3, 339-389. MR910167 (89c:16029)
    • (1987) Comment. Math. Helv. , vol.62 , Issue.3 , pp. 339-389
    • Happel, D.1
  • 32
    • 77950892360 scopus 로고    scopus 로고
    • Triangulated Calabi-Yau categories
    • to appear in the August available at the author's homepage
    • Triangulated Calabi-Yau categories, to appear in the proceedings of the workshop of the ICRA 12, Torún, August 2007, available at the author's homepage.
    • (2007) Proceedings of the Workshop of the ICRA 12, Torún
  • 33
    • 52949098045 scopus 로고    scopus 로고
    • Acyclic Calabi-Yau categories are cluster categories
    • preprint,. with an appendix by Michel Van den Bergh, MR2457529
    • Bernhard Keller and Idun Reiten, Acyclic Calabi-Yau categories are cluster categories, preprint, 2006, with an appendix by Michel Van den Bergh, Compos. Math. 144 (2008), 1332-1348. MR2457529
    • (2006) Compos. Math. , vol.144 , pp. 1332-1348
    • Keller, B.1    Reiten, I.2
  • 34
    • 33847193581 scopus 로고    scopus 로고
    • Cluster-tilted algebras are Gorenstein and stably Calabi-Yau
    • MR2313531 (2008b:18018)
    • Cluster-tilted algebras are Gorenstein and stably Calabi-Yau, Advances in Mathematics 211 (2007), 123-151. MR2313531 (2008b:18018)
    • (2007) Advances in Mathematics , vol.211 , pp. 123-151
  • 35
    • 0242287387 scopus 로고    scopus 로고
    • Generalized associahedra via quiver representations
    • DOI 10.1090/S0002-9947-03-03320-8
    • Robert Marsh, Markus Reineke, and Andrei Zelevinsky, Generalized associahedra via quiver representations, Trans. Amer. Math. Soc. 355 (2003), no. 10, 4171-4186 (electronic). MR1990581 (2004g:52014) (Pubitemid 37347182)
    • (2003) Transactions of the American Mathematical Society , vol.355 , Issue.10 , pp. 4171-4186
    • Marsh, R.1    Reineke, M.2    Zelevinsky, A.3
  • 37
    • 57049177105 scopus 로고    scopus 로고
    • Cluster characters for 2-Calabi-Yau triangulated categories
    • Cluster characters for 2-Calabi-Yau triangulated categories, Annales de l'Institut Fourier 58 (2008), no. 6, 2221-2248.
    • (2008) Annales de l'Institut Fourier , vol.58 , Issue.6 , pp. 2221-2248
  • 38
    • 0000790004 scopus 로고
    • Higher algebraic K-theory
    • I, Algebraic K-theory, I: Higher K-theories (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972), Springer-Verlag, MR0338129 (49:2895)
    • Daniel Quillen, Higher algebraic K-theory. I, Algebraic K-theory, I: Higher K-theories (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972), Lecture Notes in Math., vol. 341, Springer-Verlag, 1973, pp. 85-147. MR0338129 (49:2895)
    • (1973) Lecture Notes in Math. , vol.341 , pp. 85-147
    • Quillen, D.1
  • 40
    • 52949098546 scopus 로고    scopus 로고
    • Some remarks concerning tilting modules and tilted algebras
    • Cambridge Univ. Press, Cambridge, MR2384619 (2009b:16033)
    • Claus Michael Ringel, Some remarks concerning tilting modules and tilted algebras. Origin. Relevance. Future., Handbook of Tilting Theory, LMS Lecture Note Series, vol. 332, Cambridge Univ. Press, Cambridge, 2007, pp. 49-104. MR2384619 (2009b:16033)
    • (2007) Origin. Relevance. Future., Handbook of Tilting Theory, LMS Lecture Note Series , vol.332 , pp. 49-104
    • Michael, R.C.1
  • 41
    • 33144457634 scopus 로고    scopus 로고
    • Grassmannians and cluster algebras
    • MR2205721 (2007e:14078)
    • Joshua S. Scott, Grassmannians and cluster algebras, Proc. London Math. Soc. (3) 92 (2006), no. 2, 345-380. MR2205721 (2007e:14078)
    • (2006) Proc. London Math. Soc. (3) , vol.92 , Issue.2 , pp. 345-380
    • Scott Joshua, S.1
  • 42
    • 77950902981 scopus 로고    scopus 로고
    • The signs of Serre duality
    • Appendix A to R. Bocklandt, Graded Calabi-Yau algebras of dimension 3
    • Michel Van den Bergh, The signs of Serre duality, Appendix A to R. Bocklandt, Graded Calabi-Yau algebras of dimension 3, Journal of Pure and Applied Algebra 212 (2008), 14-32.
    • (2008) Journal of Pure and Applied Algebra , vol.212 , pp. 14-32
    • Van Den Bergh, M.1


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