A derivation is a function on an algebra which generalizes certain features of the derivative operator. Specifically, given an algebra A over a ring or field K, an K-derivation is an K-linear map D from A to itself that satisfies Leibniz's law: D(ab)=(Da)b+a(Db). More generally, an K-linear map D of A into an A-module M, satisfying the Leibniz law is also called a derivation. The collection of all K-derivation of A to itself is denoted by Der(A). The collection of K-derivations of A into an A-module M is denoted by Der(A, M ...
Read More
A derivation is a function on an algebra which generalizes certain features of the derivative operator. Specifically, given an algebra A over a ring or field K, an K-derivation is an K-linear map D from A to itself that satisfies Leibniz's law: D(ab)=(Da)b+a(Db). More generally, an K-linear map D of A into an A-module M, satisfying the Leibniz law is also called a derivation. The collection of all K-derivation of A to itself is denoted by Der(A). The collection of K-derivations of A into an A-module M is denoted by Der(A, M). Derivations occur in many different contexts in diverse areas of mathematics. If the algebra A is noncommutative, then the commutator with respect to an element of the algebra A defines a linear endomorphism of A to itself, which is a derivation over K. Furthermore, the K-module Der(A) forms a Lie algebra with respect to Lie bracket defined by the commutator: [D1, D2]=D1 D2 - D2 D1. In this book we deal with the derivations of Leibniz algebras. The Leibniz algebra is a generalization of Lie algebra, so it makes sense to study the problems related to Lie algebras for the class of Leibniz algebras.
Read Less
Add this copy of Derivations of Low-Dimensional Leibniz Algebras to cart. $115.73, new condition, Sold by Media Smart rated 4.0 out of 5 stars, ships from Hawthorne, CA, UNITED STATES, published 2012 by VDM Verlag Dr. Mueller Aktiengesellschaft & Co. KG.
Add this copy of Derivations of Low-Dimensional Leibniz Algebras: to cart. $135.33, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 2012 by LAP LAMBERT Academic Publishin.
