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

2015/02/19 by Mikhail V. Ignatyev, Mikhail Ignatyev, Ignatyev, Mikhail +2 · 1 citation
Mathematics · #17B10 #17B35 #17B65 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #math.RT #msc:17B10 #msc:17B35 #msc:17B65

paper · pdf · doi:10.48550/arxiv.1502.05486

20 pages

arxiv created 2015/02/19 · openalex publication_date 2015/02/19 · arxiv updated 2015/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the center of U(\mathfrakn), where \mathfrakn is the locally nilpotent radical of a splitting Borel subalgebra of a simple complex Lie algebra \mathfrakg=\mathfraksl_∞(ℂ), \mathfrakso_∞(ℂ), \mathfraksp_∞(ℂ). There are infinitely many isomorphism classes of Lie algebras \mathfrakn, and we provide explicit generators of the center of U(\mathfrakn) in all cases. We then fix \mathfrakn with "largest possible" center of U(\mathfrakn) and characterize the centrally generated primitive ideals of U(\mathfrakn) for \mathfrakg=\mathfraksl_∞(ℂ), \mathfraksp_∞(ℂ) in terms of the above generators. As a preliminary result, we provide a characterization of the centrally generated primitive ideals in the enveloping algebra of the nilradical of a Borel subalgebra of \mathfraksl_n(ℂ), \mathfraksp_2n(ℂ).

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

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