Examples of quantum cluster algebras associated to partial flag varieties

Details Examples of quantum cluster algebras associated to partial flag varieties Examples of quantum cluster algebras associated to partial flag varieties

2009-07-28

arxiv.org/abs/0907.4922v3

Journal of Pure and Applied Algebra, 215 (2011), no. 7, 1582-1595

Mathematics

Quantum Algebra

20 pages. Version 2: corrections to exchange relations. Version 3: general minor revisions; inclusion of exchange graph for fi

Scientific paper

10.1016/j.jpaa.2010.09.012

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 Schroer, 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.

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