132 citations · 1.9k across the 101 of their papers we have counts for
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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…
Searching for extremal PPT entangled states
Remigiusz Augusiak, Janusz Grabowski, Marek Kuś +1
We study extremality in various sets of states that have positive partial transposes. One of the tools we use for this purpose is the recently formulated criterion allowing to judg…
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…
Geometric structures encoded in the Lie structure of an Atiyah algebroid
Janusz Grabowski, Alexei Kotov, Norbert Poncin
We investigate Atiyah algebroids, i.e. the infinitesimal objects of principal bundles, from the viewpoint of Lie algebraic approach to space. First we show that if the Lie algebras…
Pontryagin Maximum Principle - a generalization
Janusz Grabowski, Michal Jozwikowski
The fundamental theorem of the theory of optimal control, the Pontryagin maximum principle (PMP), is extended to the setting of almost Lie (AL) algebroids, geometrical objects gene…
Wigner's Theorem and geometry of extreme positive maps
Janusz Grabowski, Marek Kus, Giuseppe Marmo
We consider transformation maps on the space of states which are symmetries in the sense of Wigner. Due to the convex nature of the space of states, the set of these maps has a con…