|
|
On quantum cluster algebras of finite type |
Ming DING() |
Institute for Advanced Study, Tsinghua University, Beijing 100084, China |
|
|
Abstract We extend the definition of a quantum analogue of the Caldero-Chapoton map defined by D. Rupel. When Q is a quiver of finite type, we prove that the algebra ??|k|(Q) generated by all cluster characters is exactly the quantum cluster algebra ??|k|(Q).
|
Keywords
Cluster variable
quantum cluster algebra
|
Corresponding Author(s):
DING Ming,Email:m-ding04@mails.tsinghua.edu.cn
|
Issue Date: 01 April 2011
|
|
1 |
Berenstein A, Fomin S, Zelevinsky A. Cluster algebras III: Upper bounds and double Bruhat cells. Duke Math J , 2005, 126: 1-52 doi: 10.1215/S0012-7094-04-12611-9
|
2 |
Buan A, Marsh R, Reineke M, Reiten I, Todorov G. Tilting theory and cluster combinatorics. Adv Math , 2006, 204: 572-618 doi: 10.1016/j.aim.2005.06.003
|
3 |
Berenstein A, Zelevinsky A. Quantum cluster algebras. Adv Math , 2005, 195: 405-455 doi: 10.1016/j.aim.2004.08.003
|
4 |
Caldero P, Chapoton F. Cluster algebras as Hall algebras of quiver representations. Comm Math Helv , 2006, 81: 595-616 doi: 10.4171/CMH/65
|
5 |
Caldero P, Keller B. From triangulated categories to cluster algebras. Invent Math , 2008, 172(1): 169-211 doi: 10.1007/s00222-008-0111-4
|
6 |
Ding M, Xiao J, Xu F. Integral bases of cluster algebras and representations of tame quivers. arXiv:0901.1937 [math.RT]
|
7 |
Ding M, Xu F. Bases of the quantum cluster algebra of the Kronecker quiver. arXiv:1004.2349v4 [math.RT]
|
8 |
Ding M, Xu F. The multiplication theorem and bases in finite and affine quantum cluster algebras. arXiv:1006.3928v3 [math.RT]
|
9 |
Fomin S, Zelevinsky A. Cluster algebras. I. Foundations. J Amer Math Soc , 2002, 15(2): 497-529 doi: 10.1090/S0894-0347-01-00385-X
|
10 |
Fomin S, Zelevinsky A. Cluster algebras. II. Finite type classification. Invent Math , 2003, 154(1): 63-121 doi: 10.1007/s00222-003-0302-y
|
11 |
Geiss C, Leclerc B, Schr?er J. Kac-Moody groups and cluster algebras. arXiv:1001.3545v2 [math.RT]
|
12 |
Geiss C, Leclerc B, Schr?er J. Generic bases for cluster algebras and the Chamber Ansatz. arXiv:1004.2781v2 [math.RT]
|
13 |
Grabowski J, Launois S. Quantum cluster algebra structures on quantum Grassmannians and their quantum Schubert cells: the finite-type cases. Int Math Res Notices , 2010, doi: 10.1093/imrn/rnq153
|
14 |
Hubery A. Acyclic cluster algebras via Ringel-Hall algebras. Preprint , 2005
|
15 |
Lampe P. A quantum cluster algebra of Kronecker type and the dual canonical basis. Int Math Res Notices , 2010, doi: 10.1093/imrn/rnq162
|
16 |
Qin F. Quantum cluster variables via Serre polynomials. arXiv:1004.4171v2 [math.QA]
|
17 |
Rupel D. On a quantum analogue of the Caldero-Chapoton Formula. Int Math Res Notices , 2010, doi: 10.1093/imrn/rnq192
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
|
Shared |
|
|
|
|
|
Discussed |
|
|
|
|