Abstract
AbstractWe prove that the variety of Lie algebras arising from splicing operation coincides with the variety CM of centreby-metabelian Lie algebras. Using these Lie algebras we find the minimal dimension algebras generated the variety CM and the variety of its associative envelope algebras. We study the splicing n-ary operation. We show that all n-ary (n > 2) commutator algebras arising from this operation are nilpotent of index 3. We investigate the generalization of the splicing n-ary operation, and we formulate a series of open problems.
Reference17 articles.
1. De Azcárraga J., Izquierdo J., n-ary algebras: a review with applications, J. Phys. A., 2010, 43(293001)
2. Birkhoff G., Lattice theory, Amer. Math. Soc., Providence, vol. 25, 1967
3. Bremner M.R., Jordan algebras arising from intermolecular recombination, ACM SIGSAM Bull., 2005, 39(4), 106–117
4. Bremner M., Polynomial identities for ternary intermolecular recombination, Discrete Contin. Dyn. Syst., Ser. S, 2011, 4(6), 1387–1399
5. Filippov V., n-Lie algebras. Sib. Mat. Zh, 1985, 26(6), 126–140