Isomorphism classes of 10-dimensional filiform Leibniz algebras

Citation

Mohd Kasim, Suzila and Rakhimov, Isamiddin Sattarovich and Said Husain, Sharifah Kartini (2013) Isomorphism classes of 10-dimensional filiform Leibniz algebras. In: 3rd International Conference on Mathematical Sciences (ICMS3), 17-19 Dec. 2013, Kuala Lumpur, Malaysia. (pp. 708-715).

Abstract

This paper implements Rakhimov-Bekbaev approach to present a complete list of isomorphism classes of a subclass of complex filiform Leibniz algebras obtained from naturally graded non-Lie filiform Leibniz algebra. This class is split into two subclasses. In this paper we shall consider the second class which is denoted by SLb n in dimension n. The isomorphism criteria in terms of invariant functions for SLb 10 are presented. We represent SLb10as a union of subsets and show that some of these subsets are represented as union of infinitely many orbits (a set of isomorphic to each other algebras) while others are represented as just a single orbit. In former case we give invariant functions to distinguish the orbits, while for the latter case the representatives of the single orbits are provided. As a result, we give the list of isomorphism classes with the table of multiplications.

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Additional Metadata

Item Type:	Conference or Workshop Item (Paper)
Divisions:	Faculty of Science Institute for Mathematical Research
DOI Number:	https://doi.org/10.1063/1.4882563
Publisher:	AIP Publishing LLC
Keywords:	Filiform Leibniz algebra; Invariant function; Isomorphism class; Isomorphism criteria
Depositing User:	Nurul Ainie Mokhtar
Date Deposited:	15 Sep 2016 05:03
Last Modified:	12 Sep 2017 05:40
Altmetrics:	http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.1063/1.4882563
URI:	http://psasir.upm.edu.my/id/eprint/34295
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