Malaysian Journal of Mathematical Sciences, September 2019, Vol. 13, No. 3
Classification of a Subclass of 10-Dimensional Complex Filiform Leibniz Algebras
Mohamed, N. S., Husain, S. K. S., and Rakhimov, I. S.
Corresponding Email: kartini@upm.edu.my
Received date: 12 April 2018
Accepted date: 20 July 2019
Abstract:
This article deals with the isomorphism classes and invariants of filiform Leibniz algebras arising from naturally graded non Lie filiform Leibniz algebras. It has been divided into two subclasses denoted by \(FLb_n\) and \(SLb_n\) in fixed dimension \(n\). In the paper we will focus on studying of \(FLb_n\). To study the structure of \(FLb_n\) one needs to describe its isomorphisms classes. One of the approaches to solve the isomorphism problem has been made earlier by using algebraic invariants. The paper implements the approach to \(FLb_{10}\). The isomorphism criteria by using invariant functions are given. The class \(FLb_{10}\) is split into its disjoint subsets. Some of these subset consists of a union of parametric family of orbits while the others are just single orbits. For parametric family of orbit cases, the invariants separating the orbits are given.
Keywords: Isomorphism class, isomorphism criterion, invariant function
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