Some properties of evolution algebras

Details Some properties of evolution algebras Some properties of evolution algebras

2010-04-12

arxiv.org/abs/1004.1987v1

Mathematics

Commutative Algebra

14 pages

Scientific paper

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 criteria 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 $1+2^{n-1}.$ The criteria of planarity for finite graphs is formulated by means of evolution algebras defined by graphs.

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