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arxiv: 1902.02191 · v1 · submitted 2019-02-06 · 🧮 math.RA

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Evolution algebras, automorphisms, and graphs

Alberto Elduque , Alicia Labra
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classification 🧮 math.RA
keywords algebraautomorphismsevolutiongraphabelianaffinealgebrasassociated
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The affine group scheme of automorphisms of an evolution algebra that is equal to its square, is shown to lie in an exact sequence, such that the other terms depend solely on the directed graph associated to the algebra. As a consequence, the Lie algebra of derivations is shown to be trivial in characteristic 0 or 2, and to be abelian, with a precise description depending just on the graph, otherwise.

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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.