On algebraic curves for commuting elements in $q$-Heisenberg algebras
In the present article we continue investigating the algebraic dependence of commuting elements in q-deformed Heisenberg algebras. We provide a simple proof that the 0-chain subalgebra is a maximal commutative subalgebra when q is of free type and that it coincides with the centralizer (commutant) of any one of its elements dierent from the scalar multiples of the unity. We review the Burchnall-Ch