The dimension subalgebra problem for enveloping algebras of Lie superalgebras
Author:
David M. Riley
Journal:
Proc. Amer. Math. Soc. 123 (1995), 29752980
MSC:
Primary 17B35; Secondary 16S30
MathSciNet review:
1264829
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Abstract: Let L be an arbitrary Lie superalgebra over a field of characteristic different from 2. Denote by the ideal generated by L in its universal enveloping algebra . It is shown that for each , where is the nth term of the lower central series of L. We also prove that is a residually nilpotent ideal if and only if L is residually nilpotent. Both these results remain true in characteristic 2 provided we take L to be an ordinary Lie algebra.
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 M. Lazard, Sur les groupes nilpotents et les anneaux de Lie, Ann. Sci. École Norm. Sup. 71 (1954), 101190. MR 0088496 (19:529b)
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 J. C. McConnell, The intersection theorem for a class of noncommutative rings, Proc. London Math. Soc. 17 (1967), 487498. MR 0210738 (35:1624)
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 D. G. Quillen, On the associated graded ring of a group ring, J. Algebra 10 (1968), 411418. MR 0231919 (38:245)
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 D. M. Riley, Numbers of generators of ideals in graded group rings and padic analytic prop groups of dimension one, Arch. Math. 63 (1994), 402406. MR 1300733 (96c:20056)
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 M. Scheunert, The theory of Lie superalgebras, Lecture Notes in Math., vol. 716, SpringerVerlag, Berlin, 1979. MR 537441 (80i:17005)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199512648290
PII:
S 00029939(1995)12648290
Article copyright:
© Copyright 1995 American Mathematical Society
