\(SL_ h(2)\)-symmetric torsionless connections (Q1357230)

The \(h\)-plane is a noncommutative generalization of the usual plane where the algebra of polynomial functions is generated by two variables \(x\) and \(y\) with the relation \(xy-yx= hy^2\). On the \(h\)-plane there is an action of the Jordan deformation \(SL_h (2)\) of \(SL(2)\). The authors study \(SL_h (2)\)-coinvariant, torsionless linear connections on the \(h\)-plane. They find a two-parameter family of such connections.