Evolution algebras of arbitrary dimension and their decompositions

By Yolanda Cabrera Casado, Mercedes Siles Molina, M. V. Velasco. 2016

68 citations recorded by the source corpus.

We study evolution algebras of arbitrary dimension. We analyze in deep the notions of evolution subalgebras, ideals and non-degeneracy and describe the ideals generated by one element and characterize the simple evolution algebras. We also prove the existence and unicity of a direct sum decomposition into irreducible components for every non-degenerate evolution algebra. When the algebra is degenerate, the uniqueness cannot be assured. The graph associated to an evolution algebra (relative to a natural basis) will play a fundamental role to describe the structure of the algebra. Concretely, a non-degenerate evolution algebra is irreducible if and only if the graph is connected. Moreover, when the evolution algebra is finite-dimensional, we give a process (called the fragmentation process) to decompose the algebra into irreducible components.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/06dd97381244360cd9bce100b971fe59e2bd863d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Yolanda Cabrera Casado
2. M. V. Velasco
3. Mercedes Siles Molina
4. G. Pino

In Geometry and Topology

1. Yolanda Cabrera Casado
2. M. V. Velasco
3. Mercedes Siles Molina
4. G. Pino

Citations in the corpus

• Classification of three-dimensional evolution algebras (2017, background): “Note that this definition does not depend on the basis as proved in [1].”