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- W2008409145 abstract "We define a notion of pseudo-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 $X^*=Y$, $R^*subseteq R$. We prove that a weight module $V$ is pseudo-unitarizable iff it is isomorphic to its finitistic dual $V^sharp$. Using the classification of weight modules by Drozd, Guzner and Ovsienko, we obtain necessary and sufficient conditions for an indecomposable weight module to be isomorphic to its finitistic dual, and thus to be pseudo-unitarizable. Some examples are given, including $U_q(mathfrak{sl}_2)$ for $q$ a root of unity." @default.
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- W2008409145 date "2011-10-01" @default.
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- W2008409145 title "Pseudo-unitarizable weight modules over generalized Weyl algebras" @default.
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- W2008409145 doi "https://doi.org/10.1016/j.jpaa.2010.12.015" @default.
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