Bar-invariant bases of the quantum cluster algebra of type A 2 ( 2 )

Xueqing Chen; Ming Ding; Jie Sheng

Czechoslovak Mathematical Journal (2011)

  • Volume: 61, Issue: 4, page 1077-1090
  • ISSN: 0011-4642

Abstract

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We construct bar-invariant ℤ [ q ± 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.

How to cite

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Chen, Xueqing, Ding, Ming, and Sheng, Jie. "Bar-invariant bases of the quantum cluster algebra of type $A^{(2)}_2$." Czechoslovak Mathematical Journal 61.4 (2011): 1077-1090. <http://eudml.org/doc/196683>.

@article{Chen2011,
abstract = {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.},
author = {Chen, Xueqing, Ding, Ming, Sheng, Jie},
journal = {Czechoslovak Mathematical Journal},
keywords = {quantum cluster algebra; $\mathbb \{Z\}[q^\{\pm \{1\}/\{2\}\}]$-basis; valued quiver; quantum cluster algebras; -bases; valued quivers},
language = {eng},
number = {4},
pages = {1077-1090},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Bar-invariant bases of the quantum cluster algebra of type $A^\{(2)\}_2$},
url = {http://eudml.org/doc/196683},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Chen, Xueqing
AU - Ding, Ming
AU - Sheng, Jie
TI - Bar-invariant bases of the quantum cluster algebra of type $A^{(2)}_2$
JO - Czechoslovak Mathematical Journal
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 4
SP - 1077
EP - 1090
AB - 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.
LA - eng
KW - quantum cluster algebra; $\mathbb {Z}[q^{\pm {1}/{2}}]$-basis; valued quiver; quantum cluster algebras; -bases; valued quivers
UR - http://eudml.org/doc/196683
ER -

References

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  8. Ding, M., Xu, F., Bases in quantum cluster algebra of finite and affine types, arXiv:1006.3928. 
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  12. Fomin, S., Zelevinsky, A., 10.1007/s00222-003-0302-y, Invent. Math. 154 (2003), 63-121. (2003) Zbl1054.17024MR2004457DOI10.1007/s00222-003-0302-y
  13. Geiss, C., Leclerc, B., Schröer, J., Generic bases for cluster algebras and the Chamber Ansatz, arXiv:1004.2781. MR2833478
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  17. Sherman, P., Zelevinsky, A., 10.17323/1609-4514-2004-4-4-947-974, Moscow Math. J. 4 (2004), 947-974. (2004) Zbl1103.16018MR2124174DOI10.17323/1609-4514-2004-4-4-947-974

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