2018/07/06 by María Inez Cardoso Gonçalves, Daniel Gonçalves, Gonçalves, Maria Inez Cardoso +7
Mathematics · #17A36 #17A60 #17D92 #Advanced Topics in Algebra #FOS: Mathematics #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1807.02362
openalex publication_date 2018/07/06 · openalex created_date 2022/08/04 · openalex updated_date 2026/07/28
We associate an square to any two dimensional evolution algebra. This\ngeometric object is uniquely determined, does not depend on the basis and\ndescribes the structure and the behaviour of the algebra. We determine the\nidentities of degrees at most four, as well as derivations and automorphisms.\nWe look at the group of automorphisms as an algebraic group, getting in this\nform a new algebraic invariant. The study of associative representations of\nevolution algebras is also started and we get faithful representations for most\ntwo-dimensional evolution algebras. In some cases we prove that faithful\ncommutative and associative representations do not exist, giving raise to the\nclass of what could be termed as "exceptional" evolution algebras (in the sense\nof not admitting a monomorphism to an associative algebra with deformed\nproduct).\n