RT Journal Article
T1 Tensor Product of Evolution Algebras
A1 Cabrera-Casado, Yolanda
A1 Martín-Barquero, Dolores
A1 Martín-González, Cándido
A1 Tocino-Sánchez, Alicia
K1 Productos tensoriales
K1 Álgebras genéticas
K1 Algebras no asociativas
AB 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.
PB Springer Nature
YR 2022
FD 2022-12-28
LK https://hdl.handle.net/10630/26506
UL https://hdl.handle.net/10630/26506
LA eng
NO Cabrera Casado, Y., Martín Barquero, D., Martín González, C. et al. Tensor Product of Evolution Algebras. Mediterr. J. Math. 20, 43 (2023). https://doi.org/10.1007/s00009-022-02246-5
NO Funding for open access publishing: Universidad Málaga/CBUA.
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 21 ene 2026