132 citations · 1.9k across the 101 of their papers we have counts for
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Graded quantum cluster algebras of infinite rank as colimits
Jan E. Grabowski, Sira Gratz
We provide a graded and quantum version of the category of rooted cluster algebras introduced by Assem, Dupont and Schiffler and show that every graded quantum cluster algebra of i…
A quantum analogue of the dihedral action on Grassmannians
Justin M. Allman, Jan E. Grabowski
In recent work, Launois and Lenagan have shown how to construct a cocycle twisting of the quantum Grassmannian and an isomorphism of the twisted and untwisted algebras that sends a…
Quantum cluster algebra structures on quantum Grassmannians and their quantum Schubert cells: the finite-type cases
Jan E. Grabowski, Stéphane Launois
We exhibit quantum cluster algebra structures on quantum Grassmannians and their quantum Schubert cells, as well as on , and $K_q[Gr(3,8…
Examples of quantum cluster algebras associated to partial flag varieties
Jan E. Grabowski
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 the…
Braided-Lie bialgebras associated to Kac-Moody algebras
Jan E. Grabowski
Braided-Lie bialgebras have been introduced by Majid, as the Lie versions of Hopf algebras in braided categories. In this paper we extend previous work of Majid and of ours to show…
Braided enveloping algebras associated to quantum parabolic subalgebras
Jan E. Grabowski
Associated to each subset of the nodes of a Dynkin diagram is a triangular decomposition of the corresponding Lie algebra into three subalgebras $\widetilde{…