Inspired by genetics, I defined evolution algebras and coalgebras in 2004, and published them in my book, "Evolution Algebras and Their Applications", and a journal. Since then, evolution algebras have raised some interests in mathemtaics community, and some researchers have conducted research on evolution algebras. From Dr. Utkir Rozikov, there are more than 250 publications about evolution algebras in MathSciNet upto April 2021. It seems become a sub-filed of mathematics now. In 2015, some colleagues suggested to survey new developments in evolution algebras. I thank Utkir Rozikov gave me a list of articles on evolution algebras in August 2014. I cannot maintain the list of research article published on or related to evolution algebras and coalgebras now. From Google, there are some research schools workshops were held about this algebra; some Ph.D theses were produced on this algebra.

Here is Professor Bernard Russo's homepage, he teaches evolution algebras in freshman seminar in the winter quarter of 2015 at University of California, Irvine.

Manuel Ceballos and colleagues wrote a paper "A historical perspective of Tian’s evolution algebras"

The following list of papers was updated on March, 2015.

J. P. Tian: Evolution Algebras and Their Applications (research monograph), Lecture Notes in Mathematics of Springer, vol. 1921, Springer-Verlag Heidelberg, 2008. PDF

J. Tian and B-L. Li: Coalgebraic structure of genetic inheritance, Mathematical Biosciences and Engineering, Vol. 1 (2004), no. 2, pp. 243 - 266. PDF

J. P. Tian and P. Vojtechovsky: Mathematical concepts of evolution algebras in non-Mendelian genetics, Quasigroups and related systems, Vol. 14 (2006), no. 1, pp. 111 - 122.

U. Rozikov and Jianjun Paul Tian: Evolution algebras generated by Gibbs measure, Lobachevskii Journal of Mathematics, Vol. 32 (2011), no. 4, pp. 270 - 277.

J. P. Tian: Algebraic model for non-Mendelian genetics, Discrete and Continuous Dynamical Systems - S, Vol. 4 (2010), Issue 6, pp. 1577 - 1586.

J. P. Tian and Y.M. Zou: Finitely generated nil but not nilpotent evolution algebras, Linear algebra and its applications, Vol. 13(2014), Issue 01, 10 pages, DOI: 10.1142/S0219498813500709.

M. Ladra and U.A. Rozikov: Evolution algebra of a bisexual population, Journal of Algebra, Vol. 378 (2013), 153-172.

J.M. Casas, M. Ladra, and U.A. Rozikov: A chain of evolution algebras, Linear Algebra and Its Appl, Vol. 435 (4) (2011), 852-870.

A. Labra, M. Ladra, and U.A. Rozikov: An evolution algebra in population genetics, Linear Algebra and Its Appl, Vol. 457 (2014), 348-362.

B.A. Omirov, U.A. Rozikov, and K.M. Tulenbayev: On real chains of evolution algebras, Linear and Multilinear Alg, 2014, DOI:10.1080/03081087.2014.889131

U.A. Rozikov and S.N. Murodov: Dynamics of two-dimensional evolution algebras, Lobachevskii Journal of Mathematics, Vol. 34(4) (2013), 344-358.

Rozikov U.A: Evolution operators and algebras of sex linked inheritance. Asia Paci Math. Newsletter. 2013. Vol. 3, No.1, 6-11.

M. Ladra, B.A. Omirov, and U.A. Rozikov: Dibaric and evolution algebras in biology, Lobachevskii Journal of Mathematics, Vol. 35(3) (2014), 198-210.

U.A. Rozikov and S.N. Murodov: Chain of evolution algebras of chicken population, Linear Algebra and Its Appl, Vol. 450 (2014), 186-201.

A. Dzhumadil'daev, B.A. Omirov, and U.A Rozikov: On a class of evolution algebras of "chicken" population, Inter. J. Math, 2014, DOI: 10.1142/S0129167X14500736

J.M. Casas, M. Ladra, B.A. Omirov, and U.A. Rozikov: On evolution algebras, Algebra Colloquium, Vol. 21(2) (2014), 331-342.

L. M. Camacho, J. R. Gomez, B. A. Omirov, and R. M. Turdibaev: The derivations of some evolution algebras, Linear and Multilinear Algebra, Vol. 61(3) (2013), 309-322.

L. M. Camacho, J. R. Gomez, B. A. Omirov, and R. M. Turdibaev: Some properties of evolution algebras, Bull. Korean Math. Soc, Vol. 50 (5) (2013), 1481-1494.

J.M. Casas, M. Ladra, B.A. Omirov, and U.A. Rozikov: On nilpotent index and dibaricity of evolution algebras, Linear Algebra Appl, Vol. 439 (1) (2013), 90-105.

J.C. Marcos and M.V. Velasco: The Multiplicative Spectrum and the Uniqueness of the Complete Norm Topology, Filomat, Vol. 28 (3) (2014), 473-485.

I. Paniello: Stochastic matrices arising from genetic inheritance, Linera algebara and its applications, Vol. 434 (3) (2011), 791-800.

A. Elduque and A. Labra: Evolution algebras and graphs, J of algebra and its applications, 2013, DOI: 10.1142/S0219498815501030

F. Mukhamedov and I. Qaralleh: On derivations of genetic algebras, Journal of Physics, conference series 553 (2014) 012004, DIO:10.1088/1742-6596/553/1/012004

F. Mukhamedov, B. Omirov, and I. Qaralleh: Description of three dimensional solvable evolution algebras, Int Conf. Math. Stat 2013, 2014, pp. 165-174.

J. Nunez, M. Silvero, and M.T. Villar: A particular type of non-associative algebras and graph theory, Resent Researches in Applied and Computational Mathematics, pp. 72-77.

J. Nunez, M. Luisa, R. Arevalo, M.T. Villar: Certain particular families of graphicable algebras, Applied Math. and Computation, Vol. 246 (1) (2014), 416-425.

J. Nunez, M. Silvero, and M.T. Villar: Mathematical tools for the future: graph theory and graphicable algebras, Applied Math. and Computation, Vol. 219 (11) (2013), 6113-6125.

A. Kh. Khudoyberdiyev, B. A. Omirov, and I. Qaralleh: Few remarks on evolution algebras, J. Alg and Its application, 14, 1550053 (2015) [16 pages] DOI: 10.1142/S021949881550053X

W. Wang and XL. Xin: On fuzzy filters of Heyting algebras, Discrete and Cont. Dyn. Sys. S, Vol. 4(6) (2012), 1611-1619.

Y.B. Jun and S.-Z. Song: Hesitant fuzzy prefilters and filters of EQ-algebras, Appl. Math. Sci. Vol. 9(11) (2015), 515-532.

I.P. Cabrara, P. Gutierrez, J. Martinez, M. Ojeda-Aciego: Finitary coalgebraic multisemilattices and multilattices, Appl. Math. Compu. Vol. 219(1) (2012), 31-44.

I. Paniello: Stochastic matrices arising from genetic inheritance, Linear Alg and Its Appl, Vol. 434(3) (2011), 791-800.

I. Paniello: Marginal distributions of genetic coalgebras, J. Math. Biol. Vol. 68(5) (2014), 1071-1087.

Bryan Head, An Abstraction of Evolution through Algebra, published in Reed College, 2009

Y.C. Casado, M.S. Molina, M.V. Velasco, Evolution algebras of arbitrary dimension and their decompositions, Linear Alg. and Its Appl, Vol. 495 (2016) 122-162.

R. Varro, Gonosomal algebra, Journal of Algebra, Vol. 447 (2016), 1-30.

Back to Welcome page