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TitleUniversal associative envelopes of $(n+1)$-dimensional $n$-Lie algebras.
Author(s) Murray R. Bremner, Hader A. Elgendy
TypeArticle in Journal
AbstractFor n even, we prove Pozhidaev's conjecture on the existence of associative enveloping algebras for simple n-Lie (Filippov) algebras. More generally, for n even and any (n + 1)-dimensional n-Lie algebra L, we construct a universal associative enveloping algebra U(L) and show that the natural map L → U(L) is injective. We use noncommutative Gröbner bases to present U(L) as a quotient of the free associative algebra on a basis of L and to obtain a monomial basis of U(L). In the last section, we provide computational evidence that the construction of U(L) is much more difficult for n odd.
KeywordsFree associative algebras, n-Lie (Filippov) algebras, Noncommutative Gröbner bases, Representation theory, Universal associative enveloping algebras
ISSN0092-7872; 1532-4125/e
URL http://www.tandfonline.com/doi/abs/10.1080/00927872.2011.558549
JournalCommun. Algebra
PublisherTaylor & Francis, Philadelphia, PA
Translation No
Refereed No