RT Journal Article
T1 Squares and associative representations of two dimensional evolution algebras
A1 Cardoso Gonçalves, Maria Inez
A1 Gonçalves, Daniel
A1 Martín-Barquero, Dolores
A1 Martín-González, Cándido
A1 Siles-Molina, Mercedes
K1 Álgebra
AB 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).
PB World Scientific
YR 2021
FD 2021
LK https://hdl.handle.net/10630/29705
UL https://hdl.handle.net/10630/29705
LA eng
NO 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)
NO Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) - Brasil. Junta de Andaluc ́ıa and Fondos FEDER, projects FQM-336 and FQM-7156Spanish Ministerio de Econom ́ıa y Competitividad and Fondos FEDER, project MTM2016- 76327-C3-1-P.
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 20 ene 2026