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

Autor:	Bremner, Murray R., Elgendy, Hader A.
Rok vydání:	2010
Předmět:	Mathematics - Rings and Algebras Mathematical Physics Mathematics - Representation Theory Primary 17A42. Secondary 13P10 16S30 17B35
Druh dokumentu:	Working Paper
Popis:	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. Comment: 13 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1008.1987 Zobrazit plný text záznamu View this record from Arxiv