Noetherian down-up algebras |
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| Authors: | Ellen Kirkman Ian M Musson D S Passman |
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| Institution: | Department of Mathematics, Wake Forest University, Winston-Salem, North Carolina 27109 ; Department of Mathematics, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201 ; Department of Mathematics, University of Wisconsin-Madison, Madison, Wisconsin 53706 |
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| Abstract: | Down-up algebras  were introduced by G. Benkart and T. Roby to better understand the structure of certain posets. In this paper, we prove that  is equivalent to  being right (or left) Noetherian, and also to  being a domain. Furthermore, when this occurs, we show that  is Auslander-regular and has global dimension 3. |
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