The aim of this talk is to present some links between the combinatorics involved in Morita equivalence of two classes of algebras arising in noncommutative algebraic geometry: quantum tori (or MacConnell-Pettit algebras) and deformations of type A kleinian singularities (a particular case of generalized Weyl algebras).
Quantum tori are algebras of noncommutative Laurent polynomials, and we will review in the first part of the talk their definition and properties related to Morita equivalence. Then we will define generalized Weyl algebras and give results concerning their Morita equivalence in the particular case we are interested in here.
In the last part of the talk, we will focus on the links between these two studies.
This is joint work with Andrea Solotar.