Abstract :
We give a construction of a residue complex (a minimal injective resolution) for regular algebras of dimension 2, which are twisted homogeneous coordinate rings of the projective line. Residue complexes for general twisted coordinate rings have been previously constructed by geometric methods. Our method is algebraic based on (non-commutative) localizations of the algebra at orbits of points of the projective line. Along the way we establish a unique factorization in twisted coordinate rings and a partial fraction decomposition result, which we use in our construction.
