Details:
Title  Universal associative envelopes of $(n+1)$dimensional $n$Lie algebras.  Author(s)  Murray R. Bremner, Hader A. Elgendy  Type  Article in Journal  Abstract  For n even, we prove Pozhidaev's conjecture on the existence of associative enveloping algebras for simple nLie (Filippov) algebras. More generally, for n even and any (n + 1)dimensional nLie 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.  Keywords  Free associative algebras, nLie (Filippov) algebras, Noncommutative Gröbner bases, Representation theory, Universal associative enveloping algebras  ISSN  00927872; 15324125/e 
URL 
http://www.tandfonline.com/doi/abs/10.1080/00927872.2011.558549 
Language  English  Journal  Commun. Algebra  Volume  40  Number  5  Pages  18271842  Publisher  Taylor & Francis, Philadelphia, PA  Year  2012  Edition  0  Translation 
No  Refereed 
No 
