On δ-derivations of Lie algebras and superalgebras

[摘要] We study delta derivations - a construction simultaneously generalizing derivations and centroid First we compute delta-derivations of current Lie algebras and of modular Zassenhaus algebra This enables us to provide examples of Lie algebras having 1/2-derivations which are divisors of zero thus answering negatively a question of Filippov Second we note that delta-derivations allow in some circumstances to construct examples of non-semigroup gradings of Lie algebras in addition to the recent ones discovered by Elduque Third we note that utilizing the construction of the Grassmann en velope allows to obtain results about delta-(super)derivations of Lie superalgebras from the corresponding results about lie algebras In this way we prove that prime Lie superalgebras do not possess nontrivial delta-(super)derivations generalizing the recent result of Kaygorodov (C) 2010 Elsevier Inc All rights reserved

[发布日期] 2010-12-15

[关键词] δ derivation;Witt algebra;Current Lie algebra;Non semigroup grading;Grassmann envelope