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Hopf algebras and associative representations of two-dimensional evolution algebras
Yolanda Cabrera Casado, María Inez Cardoso Gonçalves, Daniel Gonçalves +3
In this paper, we establish a connection between evolution algebras of dimension two and Hopf algebras, via the algebraic group of automorphisms of an evolution algebra. Initially,…
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…
On simple evolution algebras of dimension two and three. Constructing simple and semisimple evolution algebras
Yolanda Cabrera Casado, Dolores Martín Barquero, Cándido Martín González +1
This work classifies three-dimensional simple evolution algebras over arbitrary fields. For this purpose, we use tools such as the associated directed graph, the moduli set, induct…
On the characterization of the space of derivations in evolution algebras
Yolanda Cabrera Casado, Paula Cadavid, Mary Luz Rodiño Montoya +1
We study the space of derivations for some finite-dimensional evolution algebras, depending on the twin partition of an associated directed graph. For evolution algebras with a twi…