| Title:
|
Bar-invariant bases of the quantum cluster algebra of type $A^{(2)}_2$ (English) |
| Author:
|
Chen, Xueqing |
| Author:
|
Ding, Ming |
| Author:
|
Sheng, Jie |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
61 |
| Issue:
|
4 |
| Year:
|
2011 |
| Pages:
|
1077-1090 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We construct bar-invariant $\mathbb {Z}[q^{\pm {1}/{2}}]$-bases of the quantum cluster algebra of the valued quiver $A^{(2)}_2$, one of which coincides with the quantum analogue of the basis of the corresponding cluster algebra discussed in P. Sherman, A. Zelevinsky: Positivity and canonical bases in rank 2 cluster algebras of finite and affine types, Moscow Math. J., 4, 2004, 947–974. (English) |
| Keyword:
|
quantum cluster algebra |
| Keyword:
|
$\mathbb {Z}[q^{\pm {1}/{2}}]$-basis |
| Keyword:
|
valued quiver |
| MSC:
|
13F60 |
| MSC:
|
14M17 |
| MSC:
|
16G10 |
| MSC:
|
16G20 |
| MSC:
|
16T20 |
| MSC:
|
20G42 |
| idZBL:
|
Zbl 1240.16014 |
| idMR:
|
MR2886258 |
| DOI:
|
10.1007/s10587-011-0049-3 |
| . |
| Date available:
|
2011-12-16T15:49:48Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141808 |
| . |
| Reference:
|
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| Reference:
|
[2] Caldero, P., Chapoton, F.: Cluster algebras as Hall algebras of quiver representations.Comment. Math. Helv. 81 (2006), 595-616. Zbl 1119.16013, MR 2250855, 10.4171/CMH/65 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
