Homogenized Down-up Algebras
نویسندگان
چکیده
This paper studies two homogenizations of the down-up algebras introduced in [1]. We show that in all cases the homogenizing variable is not a zero-divisor, and that when the parameter β is non-zero, the homogenized down-up algebra is a Noetherian domain and a maximal order, and also Artin-Schelter regular, Auslander regular, and Cohen-Macaulay. We show that all homogenized down-up algebras have global dimension 4 and Gelfand-Kirillov dimension 4, and with one exception all homogenized down-up algebras are prime rings. We also exhibit a basis for homogenized down-up algebras and provide a necessary condition for a Noetherian homogenized down-up algebra to be a Hopf algebra.
منابع مشابه
Down-up Algebras
The algebra generated by the down and up operators on a differential partially ordered set (poset) encodes essential enumerative and structural properties of the poset. Motivated by the algebras generated by the down and up operators on posets, we introduce here a family of infinite-dimensional associative algebras called down-up algebras. We show that down-up algebras exhibit many of the impor...
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