Repairing noncommutative diagrams (Q1320226)

Denote by \(R_ n\) the polynomial ring over \(\mathbb{Z}\) in \(X_{ij}, Y_ 1, \dots, Y_ n\), \(\;Y_ i\) \((1 \leq i \leq n)\) indeterminate entries and \((X_{ij})\) being the alternating \(n \times n\)-matrix with indeterminate entries \(\{X_{ij} | 1\leq i < j \leq n\}\), let \(I_ n\) resp. \(J_ n\) be the ideal generated by the entries of \((Y_ 1, \dots,Y_ n) (X_{ij})\) resp. by these elements and the pfaffian of \((X_{ij})\). Certain constructions and characterizations of complexes are applied to get free resolutions of \(R_{2n}/I_{2n}\) and \(R_{2n}/J_{2n}\). -- Some homological properties follow. The author announces that she will use the results in a forthcoming paper [the author, ``Projective resolutions of generic order ideals'' (to appear)].