JP Journal of Algebra, Number Theory and Applications
Volume 43, Issue 1, Pages 23 - 52
(July 2019) http://dx.doi.org/10.17654/NT043010023 |
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DERIVATIONS IN POWER-ASSOCIATIVE EVOLUTION ALGEBRAS
Moussa Ouattara and Souleymane Savadogo
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Abstract: In this paper, we investigate the derivations in evolution algebras that are power-associative. This problem is reduced to that of power-associative evolution nilalgebras. We show how to calculate derivations in decomposable algebras. This calculation shows that it is enough to describe derivations in indecomposable evolution algebras. We first determine the derivation algebra of n-dimensional indecomposable associative evolution nilalgebras with one-dimensional annihilator. We describe the derivation algebra of indecomposable nilalgebras, up to dimension 6, that are associative or not. In each case, we give the ideal of inner derivations. |
Keywords and phrases: evolution algebra, derivation, inner derivation, power associativity, nilalgebra.
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