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2020 | OriginalPaper | Chapter

Isomorphisms of Four Dimensional Perfect Non-simple Evolution Algebras

Authors : Antonio Behn, Yolanda Cabrera Casado, Mercedes Siles Molina

Published in: Associative and Non-Associative Algebras and Applications

Publisher: Springer International Publishing

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Abstract

In this paper we complete the classification of four dimensional perfect non-simple evolution algebras (under mild conditions on the based field), started in Casado et al. (Linear Algebra and its Applications, [1]). We consider the different parametric families of evolution algebras appearing in the classification and study which algebras in the same family are isomorphic.

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next chapter Power-Associative Evolution Algebras
Literature
1.
Cabrera Casado, Y., Kanuni, M., Siles Molina, M.: Basic ideals in evolution algebras. Linear Algebra Appl. (to appear)
2.
Cabrera Casado, Y., Siles Molina, M., Velasco, M.V.: Classification of three-dimensional evolution algebras. Linear Algebra Appl. 524, 68–108 (2017)MathSciNetCrossRef
3.
Cabrera Casado, Y., Siles Molina, M., Velasco, M.V.: Evolution algebras of arbitrary dimension and their decompositions. Linear Algebra Appl. 495, 122–162 (2016)MathSciNetCrossRef
4.
Cabrera Casado, Y., Siles Molina, M.: Classification of four dimensional simple evolution algebras, Preprint
5.
6.
Casas, José M., Ladra, Manuel, Omirov, Bakhrom A., Rozikov, Utkir A.: On evolution algebras. Algebra Colloq. 21, 331–342 (2014)MathSciNetCrossRef
7.
Tian, J.P., Vojtechovsky, P.: Mathematical concepts of evolution algebras in non-Mendelian genetics. Quasigroups Relat. Syst. 14(1), 111–122 (2006)
8.
Tian, J.P.: Evolution Algebras and Their Applications. Lecture Notes in Mathematics, vol. 1921. Springer, Berlin (2008)
Metadata
Title
Isomorphisms of Four Dimensional Perfect Non-simple Evolution Algebras
Authors
Antonio Behn
Yolanda Cabrera Casado
Mercedes Siles Molina
Copyright Year
2020
Book
Associative and Non-Associative Algebras and Applications

Print ISBN: 978-3-030-35255-4

Electronic ISBN: 978-3-030-35256-1

Copyright Year: 2020

DOI
https://doi.org/10.1007/978-3-030-35256-1_1

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