Classification Of First Class Of Complex Filiform Leibniz Algebras
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Leibniz Algebras
Leibniz Algebras: Structure and Classification is designed to introduce the reader to the theory of Leibniz algebras. Leibniz algebra is the generalization of Lie algebras. These algebras preserve a unique property of Lie algebras that the right multiplication operators are derivations. They first appeared in papers of A.M Blokh in the 1960s, under the name D-algebras, emphasizing their close relationship with derivations. The theory of D-algebras did not get as thorough an examination as it deserved immediately after its introduction. Later, the same algebras were introduced in 1993 by Jean-Louis Loday , who called them Leibniz algebras due to the identity they satisfy. The main motivation for the introduction of Leibniz algebras was to study the periodicity phenomena in algebraic K-theory. Nowadays, the theory of Leibniz algebras is one of the more actively developing areas of modern algebra. Along with (co)homological, structural and classification results on Leibniz algebras, some papers with various applications of the Leibniz algebras also appear now. However, the focus of this book is mainly on the classification problems of Leibniz algebras. Particularly, the authors propose a method of classification of a subclass of Leibniz algebras based on algebraic invariants. The method is applicable in the Lie algebras case as well. Features: Provides a systematic exposition of the theory of Leibniz algebras and recent results on Leibniz algebras Suitable for final year bachelor's students, master's students and PhD students going into research in the structural theory of finite-dimensional algebras, particularly, Lie and Leibniz algebras Covers important and more general parts of the structural theory of Leibniz algebras that are not addressed in other texts
International Conference on Mathematical Sciences and Statistics 2013
Author: Adem Kilicman
language: en
Publisher: Springer Science & Business Media
Release Date: 2014-03-16
This volume is devoted to the most recent discoveries in mathematics and statistics. It also serves as a platform for knowledge and information exchange between experts from industrial and academic sectors. The book covers a wide range of topics, including mathematical analyses, probability, statistics, algebra, geometry, mathematical physics, wave propagation, stochastic processes, ordinary and partial differential equations, boundary value problems, linear operators, cybernetics and number and functional theory. It is a valuable resource for pure and applied mathematicians, statisticians, engineers and scientists.
Classification of First Class of Complex Filiform Leibniz Algebras
Author: SOZAN J. OBAIYS
language: en
Publisher: LAP Lambert Academic Publishing
Release Date: 2010-08
Leibniz algebras were introduced by J.-L.Loday. A skew-symmetric Leibniz algebra is a Lie algebra. In this case the Leibniz identity is just the Jacobi identity. This book is devoted to the classification problem of Leibiz algebra in low dimensional cases. There are two sources to get such a classification. The first of them is naturally graded non Lie filiform Leibniz algebras and the other is the naturally graded filiform Lie algebras. Here we consider Leibniz algebras appearing from the naturally graded non Lie filiform Leibniz algebras. It is known that this class of algebras can be split into two subclasses. However, isomorphisms within each class have not been investigated yet. Recently U.D.Bekbaev and I.S.Rakhimov suggested an approach to the isomorphism problem of Leibniz algebras based on algebraic invariants. This book presents an implementation of this invariant approach in 9- dimensional case. We give the list of all 9- dimensional non Lie filiform Leibniz algebras arising from the naturally graded non Lie filiform Leibniz algebras. The isomorphism criteria and the list of algebraic invariants will be given.