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Title: | The semicenter of an enveloping algebra is factorial | Authors: | Le Bruyn, Lieven OOMS, Alfons |
Issue Date: | 1985 | Publisher: | Source: | PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 93 (3) , p. 397 -397 | Abstract: | Let L be a finite-dimensional Lie algebra over a field k of characteristic zero, and U(L) its universal enveloping algebra. We show that the scmicenter of U(L) is a UFD. More generally, the same result holds when k is replaced by any factorial ring R of characteristic zero. Introduction. Throughout this note, L will be a nonzero finite-dimensional Lie algebra over a field k of characteristic zero. Let U(L) be the universal enveloping algebra of L with center Z(U(L)) and D(L) will be the division ring of quotients of U(L) with center Z(D(L)). For each X g L*, we denote by D(L)X the set of those u g D(L) such that xu-ux = X(x)u for all x g L. Its elements are called the semi-invariants of D(L) relative to X. Clearly, D(L) | Document URI: | http://hdl.handle.net/1942/37496 | ISSN: | 0002-9939 | e-ISSN: | 1088-6826 | DOI: | 10.1090/S0002-9939-1985-0773989-0 | ISI #: | A1985AEK2100004 | Rights: | 1985 American Mathematical Society | Category: | A1 | Type: | Journal Contribution |
Appears in Collections: | Research publications |
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