Delta methods in enveloping rings
type: Item
instance of: scholarly article
title: Delta methods in enveloping rings
zbMATH Open document ID: 0717.16023
DOI: 10.1016/0021-8693(90)90271-O
author: Jeffrey Bergen
author: D. S. Passman
published in: Journal of Algebra
publication date: 1990-01-01T00:00:00Z
review text: Let L be a Lie algebra over a field K of characteristic 0 with a universal enveloping algebra U(L) (or a restricted Lie algebra with restricted enveloping algebra u(L) when char K\(=p>0)\) and let L act on a K-algebra R as K-derivations. The authors consider the twisted smash products R{\#}U(L) and R{\#}u(L). The main purpose of the paper is to reduce questions about these rings to analogous ones for R{\#}U(\(\Delta\)) and R{\#}u(\(\Delta\)), where \(\Delta (L)=\{x\in L|\dim_ KL/C_ L(x)<\infty \}\) is the Lie algebra analog of the finite conjugate centre of a group. The authors establish results on annihilator ideals and primeness of R{\#}U(L) and R{\#}u(L), and on X-inner automorphisms and derivations, intersection theorems and primitivity of the twisted enveloping algebras of L.
Mathematics Subject Classification ID: 16S30
Mathematics Subject Classification ID: 16W25
Mathematics Subject Classification ID: 16S40
Mathematics Subject Classification ID: 17B35
zbMATH DE Number: 4181561
zbMATH Keywords: universal enveloping algebra
zbMATH Keywords: restricted Lie algebra
zbMATH Keywords: restricted enveloping algebra
zbMATH Keywords: K-derivations
zbMATH Keywords: twisted smash products
zbMATH Keywords: finite conjugate centre
zbMATH Keywords: annihilator ideals
zbMATH Keywords: primeness
zbMATH Keywords: X-inner automorphisms
zbMATH Keywords: primitivity
zbMATH Keywords: twisted enveloping algebras
MaRDI profile type: Publication
cites work: Identities in the universal envelopes of Lie algelras
cites work: Smash products and outer derivations
cites work: The u-Algebra of a Restricted Lie Algebra is Frobenius
cites work: Primitive group rings of soluble groups
cites work: Prime ideals in differential operator rings and crossed products of infinite groups
cites work: On the Group Ring
cites work: Ideals in group rings of free products
cites work: Representations of Restricted Lie Algebras of Characteristic p
cites work: Q5834678
cites work: X-Inner Automorphisms of Filtered Algebras
cites work: Crossed products over prime rings
cites work: Nil ideals in group rings
cites work: Primitive group rings
cites work: Observations on group rings
cites work: Infinite Crossed Products and Group-Graded Rings
cites work: Computing the symmetric ring of quotients
cites work: Group algebras
cites work: Q4769150
full work available at URL: 0021-8693(90)90271-o
OpenAlex ID: W2088465336
description: scientific article; zbMATH DE number 4181561