Centers of down-up algebras
Down-up algebras, which originated in the study of differential posets, were recently defined and studied by \textit{G. Benkart} and \textit{T. Roby} [J. Algebra 209, No. 1, 305-344 (1998; Zbl 0922.17006)]. \textit{G. Benkart} posed an open problem [Contemp. Math. 224, 29-45 (1999; Zbl 0922.17007)] to determine the centers of all down-up algebras. In this paper the author completely solves this problem. As an application, he also gets the centers of homogenizations of down-up algebras.
scientific article; zbMATH DE number 1275256
scientific article