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- W2960139114 abstract "Let $mathfrak{g}$ be a complex semisimple Lie algebra, $mathfrak{b}$ be a Borel subalgebra of $mathfrak{g}$, $mathfrak{n}$ be the nilradical of $mathfrak{b}$, and $U(mathfrak{n})$ be the universal enveloping algebra of $mathfrak{n}$. We study primitive ideals of $U(mathfrak{n})$. Almost all primitive ideals are centrally generated, i.e., are generated by their intersections with the center $Z(mathfrak{n})$ of $U(mathfrak{n})$. We present an explicit characterization of the centrally generated primitive ideals of $U(mathfrak{n})$ in terms of the Dixmier map and the Kostant cascade in the case when $mathfrak{g}$ is a simple algebra of exceptional type. (For classical simple Lie algebras, a similar characterization was obtained by Ivan Penkov and the first author.) As a corollary, we establish a classification of centrally generated primitive ideals of $U(mathfrak{n})$ for an arbitrary semisimple algebra $mathfrak{g}$." @default.
- W2960139114 created "2019-07-23" @default.
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- W2960139114 date "2019-07-07" @default.
- W2960139114 modified "2023-09-23" @default.
- W2960139114 title "Centrally generated primitive ideals of $U(mathfrak{n})$ for exceptional types" @default.
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