On Lie-admissible algebras whose commutator Lie algebras are Lie subalgebras of prime associative algebras

[摘要] We describe third power associative multiplications * on noncentral Lie ideals of prime algebras and skew elements of prime algebras with involution provided that x*y - y*x = [x,y] for all x,y and the prime algebras in question do not satisfy polynomial identities of low degree. We also obtain necessary and sufficient conditions for these multiplications to be fourth power-associative or flexible. (C) 2000 Academic Press.

[发布日期] 2000-11-15