Enveloping Algebras: Problems Old and New

  • Anthony Joseph
Part of the Progress in Mathematics book series (PM, volume 123)


I recently came across a list of twenty problems on enveloping algebras that I had presented during a meeting on Enveloping Algebras in Oberwolfach during August 1982. This was a time when the study of primitive ideals had reached a particularly interesting stage and before quantum groups had been invented. Of these roughly half were settled and need not be mentioned further. On the remaining problems relatively little progress has been made despite the availability of new geometric information particularly on orbital varieties and of our experience with quantum groups. In the following sections some of these and some new questions are reviewed. Throughout g denotes a semisimple Lie algebra and U(g) its enveloping algebra.


Quantum Group Verma Module Weight Filtration Primitive Ideal High Weight Module 
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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Anthony Joseph
    • 1
    • 2
  1. 1.Department of Theoretical MathematicsThe Weizmann Institute of ScienceRehovotIsrael
  2. 2.Laboratoire de Mathématiques FondamentalesUniversité de Pierre et Marie CurieParis 75252 Cedex 05France

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