Mathematics | |
Determining When an Algebra Is an Evolution Algebra | |
M.Victoria Velasco1  Pauline Mellon2  MiguelD. Bustamante2  | |
[1] Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain;School of Mathematics and Statistics, University College Dublin, Dublin 4, Ireland; | |
关键词: evolution algebra; multiplication structure matrices; simultaneous diagonalisation by congruence; simultaneous diagonalisation by similarity; linear pencil; | |
DOI : 10.3390/math8081349 | |
来源: DOAJ |
【 摘 要 】
Evolution algebras are non-associative algebras that describe non-Mendelian hereditary processes and have connections with many other areas. In this paper, we obtain necessary and sufficient conditions for a given algebra A to be an evolution algebra. We prove that the problem is equivalent to the so-called SDC problem, that is, the simultaneous diagonalisation via congruence of a given set of matrices. More precisely we show that an n-dimensional algebra A is an evolution algebra if and only if a certain set of n symmetric
【 授权许可】
Unknown