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

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Abstract: Let be a Lie algebra over the field of characteristic 0 and let denote its universal enveloping algebra. If is a -algebra and acts on as derivations, then there is a natural ring generated by and which is denoted by and called the smash product of by . 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 on which acts and a precisely defined one-to-one correspondence between the primes of with and the -stable primes of . Here is a Lie algebra over some field .

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DOI:
https://doi.org/10.1090/S0002-9947-1987-0891634-7

Article copyright:
© Copyright 1987
American Mathematical Society