On the semi-center of a universal enveloping algebra

DOI10.1016/0021-8693(85)90187-5zbMath0594.17010OpenAlexW1969321818MaRDI QIDQ1076785

Alfons I. Ooms, Erna Nauwelaerts, Lydia Delvaux

Publication date: 1985

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

Full work available at URL: https://doi.org/10.1016/0021-8693(85)90187-5

zbMATH Keywords

inner automorphismsuniversal enveloping algebrasemi-invariantsFrobeniusprimitiveunique factorization domainadditive subgroupsemi-centeralmost algebraic

Mathematics Subject Classification ID

Universal enveloping (super)algebras (17B35) Automorphisms, derivations, other operators for Lie algebras and super algebras (17B40) Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial) (13F15) Simple and semisimple modules, primitive rings and ideals in associative algebras (16D60) Noetherian rings and modules (associative rings and algebras) (16P40) Modules, bimodules and ideals in associative algebras (16Dxx)

Related Items (20)

On Dixmier's fourth problem ⋮ Sheets and hearts of prime ideals in enveloping algebras of semisimple Lie algebras ⋮ The hidden semi-invariants generators of an almost-Frobenius biparabolic ⋮ The Poisson center and polynomial, maximal Poisson commutative subalgebras, especially for nilpotent Lie algebras of dimension at most seven ⋮ Polynomiality of invariants, unimodularity and adapted pairs ⋮ A Negative Answer to the Problem of Dixmier on Hearts of Prime Quotients of Enveloping Algebras ⋮ Primitive localizations of an enveloping algebra ⋮ The Frobenius semiradical of a Lie algebra. ⋮ The polynomiality of the Poisson center and semi-center of a Lie algebra and Dixmier's fourth problem ⋮ Factorial domains and graded rings ⋮ The semicentre of a group algebra ⋮ A degree inequality for Lie algebras with a regular Poisson semi-center ⋮ On the weight spaces of Lie algebra modules and their Jordan kernel ⋮ On the center and semi-center of enveloping algebras in prime characteristic ⋮ Computing invariants and semi-invariants by means of Frobenius Lie algebras ⋮ The Semicenter of an Enveloping Algebra is Factorial ⋮ On the Jordan kernel of a universal enveloping algebra ⋮ Weights of Semi-Invariants of the Quotient Division Ring of an Enveloping Algebra ⋮ On certain maximal subfields in the quotient division ring of an enveloping algebra. ⋮ Semi-invariants of low-dimensional Lie algebras

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