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The starting point of this work is the fact that the class of evolution algebras over a fixed field is closed under tensor product. We prove that, under certain conditions, the tensor product is an evolution algebra if and only if every factor is an evolution algebra. Another issue arises about the inheritance of properties from the tensor product to the factors and conversely. For instance, nondegeneracy, irreducibility, perfectness and simplicity are investigated. The four-dimensional case is illustrative and useful to contrast conjectures, so we achieve a complete classification of four-dimensional perfect evolution algebras emerging as tensor product of two-dimensional ones. We find that there are four-dimensional evolution algebras that are the tensor product of two nonevolution algebras. [ABSTRACT FROM AUTHOR]

We study the space of derivations for some finite-dimensional evolution algebras, depending on the twin partition of an associated directed graph. For evolution algebras with a twin-free associated graph, we prove that the space of derivations is zero. For the remaining families of evolution algebras, we obtain sufficient conditions under which the study of such a space can be simplified. We accomplish this task by identifying the null entries of the respective derivation matrix. Our results suggest how strongly the associated graph's structure impacts in the characterization of derivations for a given evolution algebra. Therefore, our approach constitutes an alternative to the recent developments in the research of this subject. As an illustration of the applicability of our results, we provide some examples and we exhibit the classification of the derivations for non-degenerate irreducible three-dimensional evolution algebras. [ABSTRACT FROM AUTHOR]