Some quantum P-S(3) with one point

We study a certain 1-parameter Family of non-commutative graded regular alg ebras of global dimension four which were introduced by Vancliff, Van Rompa y and Willaert in [12]. Most members of the family have a singleton point s cheme of multiplicity twenty. Our objective is to analyse the point scheme of these algebras and the coordinate ring of the point scheme. In particula r, we prove that the point scheme determines the defining relations and tha t its coordinate ring is a Frobenius algebra.