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Some properties of evolution algebras
L. M. Camacho,J. R. Gomez,B. A. Omirov,R. M. Turdibaev 대한수학회 2013 대한수학회보 Vol.50 No.5
The paper is devoted to the study of finite dimensional com- plex 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 es- tablished 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 + 2n−1.
SOME PROPERTIES OF EVOLUTION ALGEBRAS
Camacho, L.M.,Gomez, J.R.,Omirov, B.A.,Turdibaev, R.M. Korean Mathematical Society 2013 대한수학회보 Vol.50 No.5
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 $1+2^{n-1}$.