9 papers
Evolution algebras: a survey of results and a list of open problems
Ivan Kaygorodov, Cándido Mart\'ın González, Antonio Viruel
Evolution algebras, introduced by J. P. Tian as an algebraic model of non- Mendelian inheritance, are commutative algebras with a basis whose distinct elements multiply to zero. Th…
Solenoids in automorphism groups of evolution algebras
Yolanda Cabrera Casado, Maria Inez Cardoso Gonçalves, Daniel Gonçalves +3
Let A be an evolution algebra (possibly infinite-dimensional) equipped with a fixed natural basis B, and let E be the associated graph defined by Elduque and Labra. We describe the…
On the socle of a class of Steinberg algebras
Lisa Orloff Clark, Cristóbal Gil Canto, Dolores Martín Barquero +2
We study minimal left ideals in Steinberg algebras of Hausdorff groupoids. We establish a relationship between minimal left ideals in the algebra and open singletons in the unit sp…
Centroid and algebraic properties of evolution algebras through graphs
Yolanda Cabrera Casado, Maria Inez Cardoso Gonçalves, Daniel Gonçalves +3
The leitmotiv of this paper is linking algebraic properties of an evolution algebra with combinatorial properties of the (possibly several) graphs that one can associate to the alg…
The algebraic entropies of the Leavitt path algebra and the graph algebras agree
Wolfgang Bock, Cristóbal Gil Canto, Dolores Martín Barquero +3
In this note we prove that the algebras and have the same entropy. Entropy is always referred to the standard filtrations in the corresponding kind of algebra. The ma…
On some structural properties of evolution algebras
Yolanda Cabrera Casado, Dolores Martín Barquero, Cándido Martín González +1
We consider the intersection of all maximal ideals of an evolution algebra and study the structure of the quotient $A/\M(A)$. In a previous work, maximal idea…
Algebraic characterisations of path algebras
Dolores Martín Barquero, Cándido Martín González, Iván Ruiz Campos
The theory of path algebras is usually circunscripted to the study of representations, usually linked to finite graphs. In our work, we focus on studying the structure of path alge…
Conservative algebras of -dimensional algebras, V
Ivan Kaygorodov, Dolores Martín Barquero, Cándido Martín González
The notion of conservative algebras appeared in a paper by Kantor in 1972. Later, he defined the conservative algebra of all algebras (i.e. bilinear maps) on the -dimensi…
Conservative algebras of -dimensional algebras, IV
Amir Fernández Ouaridi, Ivan Kaygorodov, Cándido Martín González
The notion of conservative algebras appeared in a paper by Kantor in 1972. Later, he defined the conservative algebra of all algebras (i.e. bilinear maps) on the -dimensi…