Geodesic
Chains of three-dimensional evolution algebras: a description
Filomat, Tome 34 (2020) no. 10, p. 3175

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

DOI

In this paper we describe locally all the chains of three-dimensional evolution algebras (3-dimensional CEAs). These are families of evolution algebras with the property that their structure matrices with respect to a certain natural basis satisfy the Chapman-Kolmogorov equation. We do it by describing all 3-dimensional CEAs whose structure matrices have a fixed rank equal to 3, 2 and 1, respectively. We show that arbitrary CEAs are locally CEAs of fixed rank. Since every evolution algebra can be regarded as a weighted digraph, this allows us to understand and visualize time-dependent weighted digraphs with 3 nodes.
DOI : 10.2298/FIL2010175I
Classification : 13J30, 13M05
Keywords: evolution algebra, Chapman-Kolmogorov equation, rank, chain 
Anvar Imomkulov; Victoria M Velasco. Chains of three-dimensional evolution algebras: a description. Filomat, Tome 34 (2020) no. 10, p. 3175 . doi: 10.2298/FIL2010175I
@article{10_2298_FIL2010175I,
     author = {Anvar Imomkulov and Victoria M Velasco},
     title = {Chains of three-dimensional evolution algebras: a description},
     journal = {Filomat},
     pages = {3175 },
     year = {2020},
     volume = {34},
     number = {10},
     doi = {10.2298/FIL2010175I},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2010175I/}
}
TY  - JOUR
AU  - Anvar Imomkulov
AU  - Victoria M Velasco
TI  - Chains of three-dimensional evolution algebras: a description
JO  - Filomat
PY  - 2020
SP  - 3175 
VL  - 34
IS  - 10
UR  - http://geodesic.mathdoc.fr/articles/10.2298/FIL2010175I/
DO  - 10.2298/FIL2010175I
LA  - en
ID  - 10_2298_FIL2010175I
ER  - 
%0 Journal Article
%A Anvar Imomkulov
%A Victoria M Velasco
%T Chains of three-dimensional evolution algebras: a description
%J Filomat
%D 2020
%P 3175 
%V 34
%N 10
%U http://geodesic.mathdoc.fr/articles/10.2298/FIL2010175I/
%R 10.2298/FIL2010175I
%G en
%F 10_2298_FIL2010175I

Cité par Sources :