Abstract
In this paper we study subalgebras of complex finite dimensional evolution algebras. We obtain the classification of nilpotent evolution algebras whose any subalgebra is an evolution subalgebra with a basis which can be extended to a natural basis of algebra. Moreover, we formulate three conjectures related to the description of such non-nilpotent algebras.
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Acknowledgements
The authors are grateful to Professor A.S. Dzhumadil’daev for formulation of the problem considered in the paper. This work was supported by the Grant No.0828/GF4 of Ministry of Education and Science of the Republic of Kazakhstan and by Ministerio de Economía y Competitividad (Spain), grant MTM2016-79661-P (European FEDER support included). The second named author was partially supported by IMU/CDC-program, and would like to acknowledge the hospitality of the Instituto de Matématicas de la Universidad de Sevilla (Spain).
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Presented by Jon F. Carlson.
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Camacho, L.M., Khudoyberdiyev, A.K. & Omirov, B.A. On the Property of Subalgebras of Evolution Algebras. Algebr Represent Theor 22, 281–296 (2019). https://doi.org/10.1007/s10468-018-9767-7
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DOI: https://doi.org/10.1007/s10468-018-9767-7