Invariants of domains under the actions of restricted Lie algebras
type: Item
instance of: scholarly article
title: Invariants of domains under the actions of restricted Lie algebras
zbMATH Open document ID: 0845.16033
author: Jeffrey Bergen
published in: Journal of Algebra
publication date: 1996-09-15T00:00:00Z
review text: The goal of this paper is to examine the relationship between a domain \(R\) and its subring of invariants \(R^L\), under the action of a finite-dimensional restricted Lie algebra \(L\). In Sections 2 and 3 the author proves a series of technical results involving differential identities, restricted enveloping algebras, smash products, and Frobenius algebras. These technical results all lead up to Section 4, where all of this paper's main results relating \(R\) and \(R^L\) are obtained. It is first shown that there exists a nondegenerate \((R^L, R^L)\)-bimodule ``trace-like'' map \(g : R \to R^L\) and therefore \(I \cap R^L \neq 0\), for every ideal \(I \neq 0\) of \(R\). Next, it is shown that there exists a right \(R^L\)-module embedding \(\phi\) of \(R\) into a finite direct sum of copies of \(R^L\). Using the maps \(g\) and \(\phi\), it is obtained a result which is a combination of several of the main results of this paper.
Mathematics Subject Classification ID: 16W25
Mathematics Subject Classification ID: 16S30
Mathematics Subject Classification ID: 17B35
Mathematics Subject Classification ID: 16W30
zbMATH DE Number: 848964
zbMATH Keywords: domains
zbMATH Keywords: subring of invariants
zbMATH Keywords: actions of finite-dimensional restricted Lie algebras
zbMATH Keywords: differential identities
zbMATH Keywords: restricted enveloping algebras
zbMATH Keywords: smash products
zbMATH Keywords: Frobenius algebras
reviewed by: Yueh-er Kuo
MaRDI profile type: Publication
full work available at URL: jabr.1995.1288
OpenAlex ID: W1975155769
Wikidata QID: Q115396167
DOI: 10.1006/JABR.1995.1288
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description: scientific article; zbMATH DE number 848964