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Examples of quantum cluster algebras associated to partial flag varieties

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Examples of quantum cluster algebras associated to partial flag varieties. / Grabowski, Jan.

In: Journal of Pure and Applied Algebra, Vol. 215, No. 7, 2011, p. 1582-1595.

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Grabowski, Jan. / Examples of quantum cluster algebras associated to partial flag varieties. In: Journal of Pure and Applied Algebra. 2011 ; Vol. 215, No. 7. pp. 1582-1595.

Bibtex

@article{77c8e3dc6b9c45f8b0399e12ebac5a5d,
title = "Examples of quantum cluster algebras associated to partial flag varieties",
abstract = "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 Gei{\ss}, Leclerc and Schr{\"o}er, 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. ",
author = "Jan Grabowski",
note = "The final, definitive version of this article has been published in the Journal, Journal of Pure and Applied Algebra 215 (7), 2011, {\textcopyright} ELSEVIER.",
year = "2011",
doi = "10.1016/j.jpaa.2010.09.012",
language = "English",
volume = "215",
pages = "1582--1595",
journal = "Journal of Pure and Applied Algebra",
issn = "0022-4049",
publisher = "Elsevier",
number = "7",

}

RIS

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 -