132 citations · 1.9k across the 101 of their papers we have counts for
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Automorphism groupoids in noncommutative projective geometry
Nicholas Cooney, Jan E. Grabowski
We address a natural question in noncommutative geometry, namely the rigidity observed in many examples, whereby noncommutative spaces (or equivalently their coordinate algebras) h…
Graded cluster algebras
Jan E. Grabowski
In the cluster algebra literature, the notion of a graded cluster algebra has been implicit since the origin of the subject. In this work, we wish to bring this aspect of cluster a…
Lie algebaic characterization of supercommutative space
Janusz Grabowski, Alexei Kotov, Norbert Poncin
During the last decades algebraization of space turned out to be a promising tool at the interface between Mathematics and Theoretical Physics. Starting with works by Gel'fand-Kolm…
Automorphisms of quantum and classical Poisson algebras
Janusz Grabowski, Norbert Poncin
We prove Pursell-Shanks type results for the Lie algebra D(M) of all linear differential operators of a smooth manifold M, for its Lie subalgebra D^1(M) of all linear first-order d…
Polynomial Algebras on Coadjoint Orbits of Semisimple Lie Groups
Mark J. Gotay, Janusz Grabowski, Bryon Kaneshige
We study the algebraic structure of the Poisson algebra P(O) of polynomials on a coadjoint orbit O of a semisimple Lie algebra. We prove that P(O) splits into a direct sum of its c…