RT Journal Article
T1 Evolution algebras of arbitrary dimension and their decompositions
A1 Cabrera-Casado, Yolanda
A1 Siles-Molina, Mercedes
A1 Velasco Collado, Mª Victoria
K1 Álgebra
AB We study evolution algebras of arbitrary dimension. We analyze in deep the notions of evolution subalgebras, ideals and non-degeneracy and describe the ideals generated by one element and characterize the simple evolution algebras. We also prove the existence and unicity of a direct sum decomposition into irreducible components for every non-degenerate evolution algebra. When the algebra is degenerate, the uniqueness cannot be assured.The graph associated to an evolution algebra (relative to a natural basis) will play a fundamental role to describe the structure of the algebra. Concretely, a non-degenerate evolution algebra is irreducible if and only if the graph is connected. Moreover, when the evolution algebra is finite-dimensional, we give a process (called the fragmentation process) to decompose the algebra into irreducible components.
PB Elsevier
YR 2016
FD 2016
LK https://hdl.handle.net/10630/33809
UL https://hdl.handle.net/10630/33809
LA eng
NO Yolanda Cabrera Casado, Mercedes Siles Molina, M. Victoria Velasco, Evolution algebras of arbitrary dimension and their decompositions, Linear Algebra and its Applications, Volume 495, 2016, Pages 122-162, ISSN 0024-3795, https://doi.org/10.1016/j.laa.2016.01.007
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 20 ene 2026