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Examples of quantum cluster algebras associated to partial flag varieties

Research output: Contribution to journalJournal article

Published

Journal publication date2011
JournalJournal of Pure and Applied Algebra
Journal number7
Volume215
Number of pages14
Pages1582-1595
Original languageEnglish

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 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.

Bibliographic note

The final, definitive version of this article has been published in the Journal, Journal of Pure and Applied Algebra 215 (7), 2011, © ELSEVIER.