Abstract
For generalized Weyl algebras containing the universal enveloping algebra Usl (2,K) of the Lie algebra sl (2) over a field with characteristic zero, bilateral ideals are classified. We show that a product of ideals is commutative and any proper ideal can be uniquely decomposed into a product of primary ideals.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. V. Bavula, “Description of the bilateral ideals in a certain class of noncommutative rings,”Ukr. Mat. Zh.,45, No. 2, 209–220 (1993).
Y. Nouaze' and P. Gabriel “Ideaux premiers de l'algebre enveloppante d'une algebre de Lie nilpotente,”J. Algebra,6, 77–99 (1967).
A. A. Kirillov,Elements of the Theory of Representations [in Russian], Nauka, Moscow (1972).
J. Dixmier,Algébres Enveloppantes [Russian translation], Mir, Moscow (1978).
D. Arnal and G. Pinczon, “On algebraically irreducible representations of the Lie algebra sl (2),”J. Math. Phys.,5, 350–359 (1974).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45 No. 3, pp. 307–312, March, 1993.
Rights and permissions
About this article
Cite this article
Bavula, V.V. Description of bilateral ideals in a class of noncommutative rings. II. Ukr Math J 45, 329–334 (1993). https://doi.org/10.1007/BF01061007
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01061007