Some associative algebras related to $U(\mathfrak g)$ and twisted generalized Weyl algebras

• Autores: V. Mazorchuk, M. Ponomarenko, L. Turowska
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 92, Nº 1, 2003, págs. 5-30
• Idioma: inglés
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• Resumen

  • We prove that both Mickelsson step algebras and Orthogonal Gelfand-Zetlin algebras are twisted generalized Weyl algebras. Using an analogue of the Shapovalov form we construct all weight simple graded modules and some classes of simple weight modules over a twisted generalized Weyl algebra, improving the results from [6], where a particular class of algebras was considered and only special modules were classified.