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oai:riuma.uma.es:10630/297052026-02-03T11:09:11Zcom_10630_2254col_10630_37953
RIUMA. Repositorio Institucional de la Universidad de Málaga author Cardoso Gonçalves, Maria Inez author Gonçalves, Daniel author Martín-Barquero, Dolores author Martín-González, Cándido author Siles-Molina, Mercedes 2024-02-02T11:02:27Z 2024-02-02T11:02:27Z 2021 Cardoso Gonçalves, Maria Inez, Gonçalves, Daniel, Martín-Barquero, Dolores, Martín-González, Cándido, Siles-Molina, Mercedes. Squares and associative representations of two dimensional evolution algebras. Journal of Algebra and Its ApplicationsVol. 20, No. 06, 2150090 (2021) https://hdl.handle.net/10630/29705 10.1142/S0219498821500900 We associate an square to any two dimensional evolution algebra. This geomet- ric object is uniquely determined, does not depend on the basis and describes the structure and the behaviour of the algebra. We determine the identities of degrees at most four, as well as derivations and automorphisms. We look at the group of automorphisms as an algebraic group, getting in this form a new algebraic invariant. The study of associative representations of evolution algebras is also started and we get faithful representations for most two-dimensional evolution algebras. In some cases we prove that faithful commutative and associative representations do not exist, giving raise to the class of what could be termed as “exceptional” evolution algebras (in the sense of not admitting a monomorphism to an associative algebra with deformed product). eng Álgebra Squares and associative representations of two dimensional evolution algebras journal article 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 URL https://riuma.uma.es/bitstreams/088b57d9-ac05-4b77-ab49-3163e3b559ff/download File MD5 95cefd062ea1afb7817c4fcd1597c486 445780 application/pdf Diagrams_in_evolution_algebras.pdf