Some properties of evolution algebras

L. M. Camacho; J. R. G\'omez; B. A. Omirov; R. M. Turdibaev

doi:10.4134/BKMS.2013.50.5.1481

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2013; 50(5): 1481-1494

Printed September 1, 2013

https://doi.org/10.4134/BKMS.2013.50.5.1481

Some properties of evolution algebras

L. M. Camacho, J. R. G\'omez, B. A. Omirov, and R. M. Turdibaev

Universidad de Sevilla, Universidad de Sevilla, Institute of Mathematics and Information Technologies, National University of Uzbekistan

Abstract

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Abstract

The paper is devoted to the study of finite dimensional complex evolution algebras. The class of evolution algebras isomorphic to evolution algebras with Jordan form matrices is described. For finite dimensional complex evolution algebras the criterium of nilpotency is established in terms of the properties of corresponding matrices. Moreover, it is proved that for nilpotent $n$-dimensional complex evolution algebras the possible maximal nilpotency index is $1+2^{n-1}.$

Keywords: evolution algebra, commutative algebra, isomorphism, nilpo\-tency

MSC numbers: 05C25, 17A36, 17D92, 17D99