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Zassenhaus varieties of general linear Lie algebras

Zassenhaus varieties of general linear Lie algebras
Zassenhaus varieties of general linear Lie algebras
Let g be a Lie algebra over an algebraically closed field of characteristic p>0 and let U be the universal enveloping algebra of g. We prove in this paper for g=gl_n and g=sl_n that the centre Z of U is a unique factorisation domain and that its field of fractions is rational. For g=sl_n our argument requires the assumption that p does not divide n while for g=gl_n it works for any p. It turned out that our two main results are closely related to each other. The first one confirms in type A a recent conjecture of A. Braun and C. Hajarnavis while the second answers a question of J. Alev
0021-8693
177-195
Premet, A.A.
31710c30-9fc5-44dd-a587-905f3507b5ca
Tange, R.H.
f875b810-3e2a-42ba-acd8-236b5dca9929
Premet, A.A.
31710c30-9fc5-44dd-a587-905f3507b5ca
Tange, R.H.
f875b810-3e2a-42ba-acd8-236b5dca9929

Premet, A.A. and Tange, R.H. (2005) Zassenhaus varieties of general linear Lie algebras. Journal of Algebra, 294 (1), 177-195. (doi:10.1016/j.jalgebra.2005.01.005).

Record type: Article

Abstract

Let g be a Lie algebra over an algebraically closed field of characteristic p>0 and let U be the universal enveloping algebra of g. We prove in this paper for g=gl_n and g=sl_n that the centre Z of U is a unique factorisation domain and that its field of fractions is rational. For g=sl_n our argument requires the assumption that p does not divide n while for g=gl_n it works for any p. It turned out that our two main results are closely related to each other. The first one confirms in type A a recent conjecture of A. Braun and C. Hajarnavis while the second answers a question of J. Alev

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Published date: 2005

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Local EPrints ID: 43534
URI: http://eprints.soton.ac.uk/id/eprint/43534
ISSN: 0021-8693
PURE UUID: 1e2efad4-0252-41ae-bf09-27230e895d01

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Date deposited: 23 Jan 2007
Last modified: 15 Mar 2024 08:55

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Author: A.A. Premet
Author: R.H. Tange

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