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arxiv: 1004.1987 · v1 · submitted 2010-04-12 · 🧮 math.AC

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Some properties of evolution algebras

L. M. Camacho , J. R. G\'omez , B. A. Omirov , R. M. Turdibaev
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classification 🧮 math.AC
keywords algebrasevolutioncomplexdimensionalfinitecriteriagraphsmatrices
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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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  1. Expander Evolution Algebras

    math.RA 2026-05 unverdicted novelty 8.0

    Expander evolution algebras are nonassociative algebras whose graphs are expanders, proven connected and simple with Cheeger constant controlling subalgebra structure and spectral gaps over C.