Centrally generated primitive ideals of \(U(\mathfrak{n})\) in types B and D. (English) Zbl 1466.17008
Let \(n\) is a finite-dimensional nilpotent Lie algebra. Then primitive ideals in the universal enveloping algebra \(U(n)\) can be described in terms of the Dixmier map assigning to any linear form \(f\in n^*\) a primitive ideal \(J(f)\) of \(U(n)\).
Now Let \(n\) be a nilpotent radical of the Borel subalgebra of a simple complex Lie algebra \(g=\mathfrak{so}(2n+1), \mathfrak{so}(2n),\mathfrak{so}(\infty)\). In the paper under review a description of primitive ideals ananlogous to Dixmier’s description.
Now Let \(n\) be a nilpotent radical of the Borel subalgebra of a simple complex Lie algebra \(g=\mathfrak{so}(2n+1), \mathfrak{so}(2n),\mathfrak{so}(\infty)\). In the paper under review a description of primitive ideals ananlogous to Dixmier’s description.
Reviewer: Dmitry Artamonov (Moskva)
MSC:
| 17B65 | Infinite-dimensional Lie (super)algebras |
| 17B35 | Universal enveloping (super)algebras |
| 17B10 | Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) |
| 17B08 | Coadjoint orbits; nilpotent varieties |
| 17B20 | Simple, semisimple, reductive (super)algebras |
Keywords:
Dixmier map; Kostant cascade; center of enveloping algebra; centrally generated primitive ideal; locally nilpotent Lie algebraReferences:
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