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

Issue

Vol. 92 No. 1 (2003)

Section

Articles

How to Cite

[1]
V. Mazorchuk, M. Ponomarenko, and L. Turowska, “Some associative algebras related to $U(\mathfrak g)$ and twisted generalized Weyl algebras”, Math. Scand., vol. 92, no. 1, pp. 5–30, Mar. 2003, doi: 10.7146/math.scand.a-14392.