The skew field of rational functions on the quantum plane (Q1296165)

Let \(k\) be a (commutative) field. The authors investigate certain properties of the quantum field \(k_q(X,Y)\), that is the skew field of fractions of the quantum algebra \(k_q[X,Y]\) (with relation \(XY=qYX\)), \(q\) is not a root of unity. They prove that in \(k_q(X,Y)\) the centralizer of any element outside \(k\) is commutative. All automorphisms of \(k_q(X,Y)\) are described. There are also listed 3 open problems on this subject.