Irreducible components of module varieties: An example

We determine the irreducible components of the variety of d-dimensional modules over the algebra k〈α,β〉/〈α2,β2,βα+qαβ〉 with q∈k⁎, for any d, and we describe any intersection of irreducible components as the zero set of some ideal. We show that any such intersection is irreducible. To our knowledge, this is the first time irreducible components are described by equations for modules over an algebra which is neither representation finite nor hereditary.