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On properties of some nilpotent evolution algebras and their enveloping algebras

Ahmad Alarafeen

School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia

E-mail Address: ahmadalarfeen@gmail.com

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Azhana Ahmad

https://orcid.org/0000-0002-0726-3183

School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia

E-mail Address: azhana@usm.my

Corresponding author.

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, and

Izzat Qaralleh

Department of Mathematics, Faculty of Science, Tafila Technical University, Tafila, Jordan

E-mail Address: izzat_math@yahoo.com

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https://doi.org/10.1142/S0219498823502596Cited by:0 (Source: Crossref)

Abstract

In this paper, we consider $n$ $n$ -dimensional nilpotent finite-dimensional evolution algebras with non-maximal index of nilpotency. We give complete invariants of these algebras in order to classify them. Then, we describe their associative enveloping algebras. We also give a positive answer to the question whether a derivation of this nilpotent evolution algebra is possible to be extended to its enveloping algebra.

Communicated by Rachel Camina

Keywords:

AMSC: 17D92

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