Evolution algebras satisfying a train identity of degree 2 and
exponent m>3
Savadogo Souleymane\,^1, Tenkodogo Joseph\,^2 and Conseibo André\,^3
\,^{1,2,3} Département de Mathématiques, Université Norbert ZONGO, Burkina Faso.
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Pages 275-291 | Received 06 January 2025, Accepted 29 May 2025, Published 26 January 2026
Abstract
The present paper is devoted to the study of evolution algebras that satisfy the identity x^mx^m=\omega(x)^mx^m, where the integer m>3. This polynomial identity is known as the train identity of degree 2 and exponent m. We determine the Peirce decomposition, the set of nonzero idempotents and characterise the derivations and automorphisms of the algebras of this class. In passing, we show that they strictly contain the class of finite-dimensional baric evolution algebras that are power-associative. Finally, we provide the classification of evolution algebras of dimension at most 5 that satisfy strictly the train identity of degree 2 and exponent m, for some integer m>3.
Keywords: Bernstein algebra, Evolution algebra, Train identity of degree 2 and exponent m, Peirce decomposition, Derivation, Idempotent.
MSC numbers: Primary 17A30, 17D92 ; Secondary 17A60, 17D99.
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