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A multiplication formula for module subcategories of Ext-symmetry
Author(s):
Jie
Xiao;
Fan
Xu
Journal:
Proc. Amer. Math. Soc.
137
(2009),
2517-2528.
MSC (2000):
Primary 16G20, 14M99;
Secondary 20G05
Posted:
March 17, 2009
MathSciNet review:
2497463
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Abstract:
We define evaluation forms associated to objects in a module subcategory of Ext-symmetry generated by finitely many simple modules over a path algebra with relations and prove a multiplication formula for the product of two evaluation forms. It is analogous to a multiplication formula for the product of two evaluation forms associated to modules over a preprojective algebra given by Geiss, Leclerc and Schröer in Compositio Math. 143 (2007), 1313-1334.
References:
-
- 1.
- P. Caldero, F. Chapoton, Cluster algebras as Hall algebras of quiver representations, Comm. Math. Helv. 81 (2006), 595-616. MR 2250855 (2008b:16015)
- 2.
- P. Caldero, B. Keller, From triangulated categories to cluster algebras, Inv. Math. 172 (2008), 169-211. MR 2385670
- 3.
- W. Crawley-Boevey, On the exceptional fibres of Kleinian singularities, Amer. J. Math. 122 (2000), no. 5, 1027-1037. MR 1781930 (2001f:14009)
- 4.
- W. Crawley-Boevey, M. Holland, Noncommutative deformations of Kleinian singularities, Duke Math. J. 92 (1998), no. 3, 605-635. MR 1620538 (99f:14003)
- 5.
- A. Dimca, Sheaves in topology. Universitext. Springer-Verlag, Berlin, 2004. MR 2050072 (2005j:55002)
- 6.
- M. Ding, J. Xiao, F. Xu, Realizing enveloping algebras via varieties of modules, arXiv:math/0604560.
- 7.
- C. Geiss, B. Leclerc, J. Schröer, Semicanonical bases and preprojective algebras, II: A multiplication formula, Compositio Mathematica 143 (2007), 1313-1334. MR 2360317 (2009b:17031)
- 8.
- A. Hubery, Acyclic cluster algebras via Ringel-Hall algebras, preprint.
- 9.
- D. Joyce, Constructible functions on Artin stacks, J. London Math. Soc. (2) 74 (2006), 583-606. MR 2286434 (2008b:14001)
- 10.
- R. D. MacPherson, Chern classes for singular algebraic varieties, Ann. of Math. (2) 100 (1974), 423-432. MR 0361141 (50:13587)
- 11.
- Ch. Riedtmann, Lie algebras generated by indecomposables, J. Algebra 170 (1994), 526-546. MR 1302854 (96e:16013)
- 12.
- C. M. Ringel, The preprojective algebra of a quiver. In: Algebras and modules II (Geiranger, 1996), 467-480, CMS Conf. Proc. 24, Amer. Math. Soc., Providence, RI, 1998. MR 1648647 (99i:16031)
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Additional Information:
Jie
Xiao
Affiliation:
Department of Mathematics, Tsinghua University, Beijing 100084, People's Republic of China
Email:
jxiao@math.tsinghua.edu.cn
Fan
Xu
Affiliation:
Department of Mathematics, Tsinghua University, Beijing 100084, People's Republic of China
Email:
fanxu@mail.tsinghua.edu.cn
DOI:
10.1090/S0002-9939-09-09886-4
PII:
S 0002-9939(09)09886-4
Keywords:
Ext-symmetry,
module variety,
flag variety,
composition series.
Received by editor(s):
January 18, 2008,
Received by editor(s) in revised form:
September 26, 2008
Posted:
March 17, 2009
Additional Notes:
The research was supported in part by NSF of China (No. 10631010)
Communicated by:
Martin Lorenz
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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