Osterburg, James; Passman, D. S. X-inner automorphisms of enveloping rings. (English) Zbl 0744.16017 J. Algebra 130, No. 2, 412-434 (1990). Summary: We determine the \(X\)-inner automorphisms of the smash product \(R\# U(L)\) of a prime ring \(R\) by the universal enveloping algebra \(U(L)\) of a characteristic 0 Lie algebra \(L\). Specifically, we show that any such automorphism \(\sigma\) stabilizing \(R\) can be written as a product \(\sigma=\sigma_ 1\sigma_ 2\), where \(\sigma_ 1\) is induced by conjugation by a unit of \(Q_ s(R)\), the symmetric Martindale ring of quotients of \(R\), and \(\sigma_ 2\) is induced by conjugation by a unit of \(Q_ s(T)\). Here \(S=Q_ l(R)\) is the left Martindale ring of quotients of \(R\) and \(T\) is the centralizer of \(S\) in \(S\#U(L)\supseteq R\#U(L)\). One of the subtleties of the proof is that we must work in several unrelated overrings of \(R\#U(L)\). Cited in 3 Documents MSC: 16S40 Smash products of general Hopf actions 17B35 Universal enveloping (super)algebras 16W20 Automorphisms and endomorphisms 16N60 Prime and semiprime associative rings 16S30 Universal enveloping algebras of Lie algebras 16S90 Torsion theories; radicals on module categories (associative algebraic aspects) Keywords:\(X\)-inner automorphisms; smash product; prime ring; universal enveloping algebra; symmetric Martindale ring of quotients; induced by conjugation PDFBibTeX XMLCite \textit{J. Osterburg} and \textit{D. S. Passman}, J. Algebra 130, No. 2, 412--434 (1990; Zbl 0744.16017) Full Text: DOI References: [1] Bergen, J.; Montgomery, S., Smash products and outer derivations, Israel J. Math., 53, 321-345 (1986) · Zbl 0602.16007 [2] Montgomery, S., \(X\)-inner automorphisms of filtered algebras, (Proc. Amer. Math. Soc., 83 (1981)), 263-268 · Zbl 0474.16003 [3] Montgomery, S., \(X\)-inner automorphisms of filtered algebras, II, (Proc. Amer. Math. Soc., 87 (1983)), 569-575 · Zbl 0509.16018 [4] Passman, D. S., Prime ideals in enveloping rings, Trans. Amer. Math. Soc., 302, 535-560 (1987) · Zbl 0628.16020 [5] Passman, D. S., Infinite Crossed Products (1989), Academic Press: Academic Press San Diego, CA · Zbl 0519.16010 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.