Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Prime ideals in enveloping rings


Author: D. S. Passman
Journal: Trans. Amer. Math. Soc. 302 (1987), 535-560
MSC: Primary 17B35; Secondary 16A33, 16A66
DOI: https://doi.org/10.1090/S0002-9947-1987-0891634-7
MathSciNet review: 891634
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $L$ be a Lie algebra over the field $K$ of characteristic $0$ and let $U(L)$ denote its universal enveloping algebra. If $R$ is a $K$-algebra and $L$ acts on $R$ as derivations, then there is a natural ring generated by $R$ and $U(L)$ which is denoted by $R\# U(L)$ and called the smash product of $R$ by $U(L)$. The aim of this paper is to describe the prime ideals of this algebra when it is Noetherian. Specifically we show that there exists a twisted enveloping algebra $U(X)$ on which $L$ acts and a precisely defined one-to-one correspondence between the primes $P$ of $R\#U(L)$ with $P \cap R = 0$ and the $L$-stable primes of $U(X)$. Here $X$ is a Lie algebra over some field $C \supseteq K$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 17B35, 16A33, 16A66

Retrieve articles in all journals with MSC: 17B35, 16A33, 16A66


Additional Information

Article copyright: © Copyright 1987 American Mathematical Society