Quiver Generalized Weyl Algebras, Skew Category Algebras and Diskew Polynomial Rings
نویسندگان
چکیده
منابع مشابه
Generalized Weyl algebras and diskew polynomial rings
The aim of the paper is to extend the class of generalized Weyl algebras to a larger class of rings (they are also called generalized Weyl algebras) that are determined by two ring endomorphisms rather than one as in the case of ‘old’ GWAs. A new class of rings, the diskew polynomial rings, is introduced that is closely related to GWAs (they are GWAs under a mild condition). The, so-called, amb...
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We define an analogue of BGG category O for generalized Weyl algebras. We prove several properties that show that even when the dimension of the ground ring is greater than one, the (graded) representation theory still has the flavor of the infinite dimensional representation theory of semisimple lie algebras. We then apply these results to the strong graded Morita problem for GWAs and give a c...
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We define a notion of unitarizability for weight modules over a generalized Weyl algebra (of rank one, with commutative coeffiecient ring R), which is assumed to carry an involution of the form X∗ = Y , R∗ ⊆ R. We prove that a weight module V is unitarizable iff it is isomorphic to its finitistic dual V . Using the classification of weight modules by Drozd, Guzner and Ovsienko, we obtain necess...
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ژورنال
عنوان ژورنال: Mathematics in Computer Science
سال: 2017
ISSN: 1661-8270,1661-8289
DOI: 10.1007/s11786-017-0313-5