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

Authors

  • V. Mazorchuk
  • M. Ponomarenko
  • L. Turowska

DOI:

https://doi.org/10.7146/math.scand.a-14392

Abstract

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.

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Published

2003-03-01

How to Cite

Mazorchuk, V., Ponomarenko, M., & Turowska, L. (2003). Some associative algebras related to $U(\mathfrak g)$ and twisted generalized Weyl algebras. MATHEMATICA SCANDINAVICA, 92(1), 5–30. https://doi.org/10.7146/math.scand.a-14392

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Articles