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oai:riuma.uma.es:10630/297052026-02-03T11:09:11Zcom_10630_2254col_10630_37953

Squares and associative representations of two dimensional evolution algebras Cardoso Gonçalves, Maria Inez Gonçalves, Daniel Martín-Barquero, Dolores Martín-González, Cándido Siles-Molina, Mercedes Álgebra Evolution algebra Associative and commutative representation 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). Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) - Brasil. Junta de Andaluc ́ıa and Fondos FEDER, projects FQM-336 and FQM-7156 Spanish Ministerio de Econom ́ıa y Competitividad and Fondos FEDER, project MTM2016- 76327-C3-1-P. 2024-02-02T11:02:27Z 2024-02-02T11:02:27Z 2024-02-02 2021 journal article SMUR 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 eng open access application/pdf World Scientific