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Pseudo-unitarizable weight modules over generalized Weyl algebras

Jonas T. Hartwig (Institutionen för matematiska vetenskaper, matematik)
Journal of Pure and Applied Algebra (0022-4049). Vol. 215 (2011), 10, p. 2352-2377.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: down-up algebras, representations

Denna post skapades 2011-06-09.
CPL Pubid: 141451


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