FEIGIN-FUKS REPRESENTATIONS FOR NONEQUIVALENT ALGEBRAS OF N=4 SUPERCONFORMAL SYMMETRY

The N=4 SU (2)k superconformal algebra has the global automorphism of SO(4)≈ SU ((2)× SU ((2) with the left factor as the Kac-Moody gauge symmetry. As a consequence, an infinite set of independent algebras labeled by ρ corresponding to the conjugate classes of the outer automorphism group SO (4)/SU(2)= SU (2) are obtained à la Schwimmer and Seiberg. We construct Feigin-Fuks representations with the ρ parameter embedded for the infinite set of the N =4 nonequivalent algebras. In our construction the extended global SU(2) algebras labeled by ρ are self-consistently represented by fermion fields with appropriate boundary conditions.

Factor-Correspondences in Regular Rings

Factor-correspondences are nothing more than a way of describing isomorphisms between principal ideals in a regular ring. However, due to a remarkable decomposition theorem of M. J. Wonenburger [7, Lemma 1], they have proved to be a highly effective tool in the study of completeness properties in matrix rings over regular rings [7, Theorem 1]. Factor-correspondences also figure in the proof of D. Handelman's theorem that an ℵ0-continuous regular ring is unitregular [4, Theorem 3.2].The aim of the present article is to sharpen the main result in [7] and to re-examine its applications to matrix rings. The basic properties of factor-correspondences are reviewed briefly for the reader's convenience.Throughout, R denotes a regular ring (with unity).Definition 1 (cf. [5, p. 209ff], [7, p. 212]). A right factor-correspondence in R is a right R-isomorphism φ : J → K, where J and K are principal right ideals of R (left factor-correspondences are defined dually).