On Evolution Algebras-Reference-Cited by-同舟云学术

On Evolution Algebras

Published:2014-04-11 Issue:02 Volume:21 Page:331-342
ISSN:1005-3867
Container-title:Algebra Colloquium
language:en
Short-container-title:Algebra Colloq.

Author:

Casas J. M.¹,Ladra M.²,Omirov B. A.³,Rozikov U. A.³

Affiliation:

1. Department of Applied Mathematics, E.U.I.T. Forestal, Pontevedra, University of Vigo, 36005, Spain

2. Department of Algebra, University of Santiago de Compostela, 15782, Spain

3. Institute of Mathematics, Tashkent, 100125, Uzbekistan

Abstract

The structural constants of an evolution algebra are given by a quadratic matrix. In this work we establish an equivalence between nil, right nilpotent evolution algebras and evolution algebras defined by upper triangular matrices. The classification of 2-dimensional complex evolution algebras is obtained. For an evolution algebra with a special form of the matrix, we describe all its isomorphisms and their compositions. We construct an algorithm running under Mathematica which decides if two finite dimensional evolution algebras are isomorphic.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1005386714000285

Reference3 articles.

1. SOME PROPERTIES OF EVOLUTION ALGEBRAS

2. The algebraic and geometric classification of associative algebras of dimension five

3. Evolution algebras generated by Gibbs measures

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1. Peirce Decompositions for Evolution Algebras;Mathematica Slovaca;2023-12-01

2. On exp(Der(E)) of nilpotent evolution algebras of maximal nilindex;Linear and Multilinear Algebra;2023-09-27

3. Tensor product of finite dimensional nilpotent evolution algebras;Journal of Algebra and Its Applications;2023-08-21

4. On Extendibility of Evolution Subalgebras Generated by Idempotents;Mathematics;2023-06-19

5. A Characterization of Associative Evolution Algebras;Contemporary Mathematics;2023-02-17