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Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Examples of quantum cluster algebras associated to partial flag varieties
AU - Grabowski, Jan
N1 - The final, definitive version of this article has been published in the Journal, Journal of Pure and Applied Algebra 215 (7), 2011, © ELSEVIER.
PY - 2011
Y1 - 2011
N2 - We give several explicit examples of quantum cluster algebra structures, as introduced by Berenstein and Zelevinsky, on quantized coordinate rings of partial flag varieties and their associated unipotent radicals. These structures are shown to be quantizations of the cluster algebra structures found on the corresponding classical objects by Geiß, Leclerc and Schröer, whose work generalizes that of several other authors. We also exhibit quantum cluster algebra structures on the quantized enveloping algebras of the Lie algebras of the unipotent radicals.
AB - We give several explicit examples of quantum cluster algebra structures, as introduced by Berenstein and Zelevinsky, on quantized coordinate rings of partial flag varieties and their associated unipotent radicals. These structures are shown to be quantizations of the cluster algebra structures found on the corresponding classical objects by Geiß, Leclerc and Schröer, whose work generalizes that of several other authors. We also exhibit quantum cluster algebra structures on the quantized enveloping algebras of the Lie algebras of the unipotent radicals.
U2 - 10.1016/j.jpaa.2010.09.012
DO - 10.1016/j.jpaa.2010.09.012
M3 - Journal article
VL - 215
SP - 1582
EP - 1595
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
SN - 0022-4049
IS - 7
ER -