Momentum Operators on Continuous Markov Evolution Algebras

Autores/as

  • Sandra M. Zapata Yepes
  • Cristian F. Coletti

Resumen

In this work we introduce the notion of momentum operator on a family of evolution algebras indexed by a time-parameter t ≥ 0. Also, we study its spectra in the case of finte-dimensional evolution algebra. Thus, this work is naturally divided into two parts. In the first part we give the main definitions on (continuous-time) Markov evolution algebras and we present some basic results on these algebras. For more details on continuous evolution algebras see [6, 7]. In the second part, we introduce the notion of momentum operator on such structures. In [5] the author study these operator on finite graphs. Then we proceed to determine its spectra in the context of continuous-time Markov evolution algebras.

Descargas

Los datos de descargas todavía no están disponibles.

Biografía del autor/a

Sandra M. Zapata Yepes

CMCC-UFABC, Santo André, SP.

Cristian F. Coletti

CMCC-UFABC, Santo André, SP.

Citas

Cadavid, P., Montoya, MLR, Rodríguez, PM. (2020). The connection between evolution algebras, random walks and graphs. J. Algebra Appl, 19.

Coletti, C. F., Carneiro, R. P., Yepes, S. Z. (2020). Some geometric properties of stochastic matrices. Proceeding Series of the Brazilian Society of Computational and Applied Mathematics, 7(1).

Coletti, C. F., De Lima, L. R., Luiz, D. A. (2022). Infinite-Dimensional Genetic and Evolution Algebras Generated by Gibbs Measures, arXiv.2212.06450

Elduque, A., Labra, A. (2015). Evolution algebras and graphs. J. Algebra Appl, 14(7).

Exner, P., (2012). Momentum Operators on graphs. arXiv 1205.5941v2

Montaner, F., Paniello, I. (2022). Continuous evolution algebras. arXiv 2202.02803v1

Paniello, I. (2021). Marcov evolution algebras. Linear and multilinear algebra, 1-21. DOI 10.1080/03081087.2021.1893636.

Tian, JP. (2008). Evolution algebras and their applications. Berlin: Springer; (Lecture notes in mathematics; 1921).

Tian, JP., Vojtechovsky, P. (2006). Mathematical concepts of evolution algebras in non-Mendelian genetics. Quasigroups Relat syst, 14(1), 11-122.

Vidal, S. J., Cadavid, P., Rodriguez, P. M. (2022) On the Hilbert evolution algebras of a graph. Sib. Math. J., 63(5):995–1011.

Descargas

Publicado

2023-12-18

Número

Sección

Resumos