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Derivations of low-dimensional Leibniz Algebras


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  • Product Description

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.

Product Specifications
SKU :COC24434
AuthorIsamiddin S.Rakhimov,Al Hossain Al Nashri and Kamel A. Mohd Atan
Number of Pages196
Publishing Year6/22/2012
Edition1 st
Book TypeMathematics
Country of ManufactureIndia
Product BrandLAP LAMBERT Academic Publishing
Product Packaging InfoBox
In The Box1 Piece
Product First Available On ClickOnCare.com2015-07-28 00:00:00