Pseudo-unitarizable weight modules over generalized Weyl algebras
Journal article, 2011

We define a notion of pseudo-unitarizability for weight modules over a generalized Weyl algebra (of rank one, with commutative coefficient ring R), which is assumed to carry an involution of the form X* = Y, R* subset of R. We prove that a weight module V is pseudo-unitarizable iff it is isomorphic to its finitistic dual V-#. 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-g (sl(2)) for q a root of unity. (C) 2010 Elsevier B.V. All rights reserved.

down-up algebras



Jonas Hartwig

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Journal of Pure and Applied Algebra

0022-4049 (ISSN)

Vol. 215 10 2352-2377

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