CENTERS OF DOWN-UP ALGEBRAS OVER FIELDS OF PRIME CHARACTERISTIC

ABSTRACT

We consider down-up algebras as defined by Benkart and Roby over ground fields of characteristic p and find the centers of those algebras. The method used here also illustrates a way of computing the center of a down-up over a field of characteristic 0 different from the ones used by Zhao [5] and by Kulkarni [3].

ACKNOWLEDGMENTS

The author wishes to thank Georgia Benkart who offered many insights and suggestions which have greatly improved the clarity of this paper.

The author acknowledges support from National Science Foundation Grant DMS-9970119 and the University of Wisconsin, Madison. This work constitutes part of the author's doctoral thesis under the direction of Georgia Benkart at the University of Wisconsin, Madison.