Centrally generated primitive ideals of U(\mathfrakn) in types B and D

2017/09/26 by Mikhail V. Ignatyev, Ignatyev, Mikhail V. · 1 citation
Mathematics · #17B08 #17B10 #17B35 #17B65 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:17B08 #msc:17B10 #msc:17B35 #msc:17B65

paper · pdf · doi:10.48550/arxiv.1709.09543

22 pages. arXiv admin note: text overlap with arXiv:1502.05486

openalex publication_date 2017/09/26 · arxiv created 2018/11/05 · arxiv updated 2018/11/06 · openalex created_date 2022/09/05 · openalex updated_date 2026/07/28

Abstract

We study the centrally generated primitive ideals of U(\mathfrakn), where \mathfrakn is the (locally) nilpotent radical of a (splitting) Borel subalgebra of a simple complex Lie algebra \mathfrakg=\mathfrako_2n+1(ℂ), \mathfrako_2n(ℂ), \mathfrako_∞(ℂ). In the infinite-dimensional setting, there are infinitely many isomorphism classes of Lie algebras \mathfrakn, and we fix \mathfrakn with "largest possible" center of U(\mathfrakn). We characterize the centrally generated primitive ideals of U(\mathfrakn) in terms of the Dixmier map and the Kostant cascade.

Citations

• Infinite Kostant cascades and centrally generated primitive ideals of U(\mathfrakn) in types A_∞, C_∞

Cited by

• Centrally generated primitive ideals of U(\mathfrakn) for exceptional types

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