The dimension subalgebra problem for enveloping algebras of Lie superalgebras

Author:
David M. Riley

Journal:
Proc. Amer. Math. Soc. **123** (1995), 2975-2980

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 *n*th 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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DOI:
https://doi.org/10.1090/S0002-9939-1995-1264829-0

Article copyright:
© Copyright 1995
American Mathematical Society