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arXiv · 1008.1987

Universal associative envelopes of (n+1)-dimensional n-Lie algebras

Murray R. Bremner·Hader A. Elgendy
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Abstract

For n even, we prove Pozhidaev's conjecture on the existence of associative enveloping algebras for simple n-Lie 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 from L to U(L) is injective. We use noncommutative Grobner 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.

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BibTeXRIS

Murray R. Bremner, Hader A. Elgendy. 2010-08-11. Universal associative envelopes of (n+1)-dimensional n-Lie algebras. https://arxiv.org/abs/1008.1987

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