Centrally generated primitive ideals of \(U(\mathfrak{n})\) for exceptional types

DOI10.1016/j.jalgebra.2020.08.015zbMath1465.17014arXiv1907.04219OpenAlexW3083544818MaRDI QIDQ2204857

Aleksandr A. Shevchenko, Mikhail V. Ignatyev

Publication date: 16 October 2020

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.04219

zbMATH Keywords

nilpotent Lie algebraexceptional root systemcenter of enveloping algebracentrally generated primitive idealDixmier mapKostant cascade

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Universal enveloping (super)algebras (17B35) Exceptional (super)algebras (17B25) Coadjoint orbits; nilpotent varieties (17B08)

Uses Software

• Python

Cites Work

• Infinite Kostant cascades and centrally generated primitive ideals of \(U(\mathfrak{n})\) in types \(A_\infty\), \(C_\infty\)
• Primideale in Einhüllenden auflösbarer Lie-Algebren (Beschreibung durch Bahnenräume)
• Primitive ideals in enveloping algebras
• A preparation theorem for the prime spectrum of a semisimple Lie algebra
• Basic sums of coadjoint orbits of the unitriangular group
• Centrally generated primitive ideals of \(U(\mathfrak{n})\) in types B and D
• Involutions in \(S_n\) and associated coadjoint orbits
• Représentations irréducibles des algèbres de Lie resolubles
• Center $$U(\mathfrak{n})$$ , Cascade of Orthogonal Roots, and a Construction of Lipsman–Wolf
• Orthogonal subsets of root systems and the orbit method
• UNITARY REPRESENTATIONS OF NILPOTENT LIE GROUPS
• The minimal orbit in a simple Lie algebra and its associated maximal ideal
• The cascade of orthogonal roots and the coadjoint structure of the nilradical of a Borel subgroup of a semisimple Lie group
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