Universal Associative Envelopes of (n+Â 1)-Dimensional n-Lie Algebras

摘要

For 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.View full textDownload full textKey WordsFree associative algebras, n-Lie (Filippov) algebras, Noncommutative Gröbner bases, Representation theory, Universal associative enveloping algebras2000 Mathematics Subject ClassificationPrimary 17A42, Secondary 13P10, 16S30, 17B35Related var addthis_config = { ui_cobrand: "Taylor & Francis Online", services_compact: "citeulike,netvibes,twitter,technorati,delicious,linkedin,facebook,stumbleupon,digg,google,more", pubid: "ra-4dff56cd6bb1830b" }; Add to shortlist Link Permalink http://dx.doi.org/10.1080/00927872.2011.558549