© 2008

Evolution Algebras and their Applications


Part of the Lecture Notes in Mathematics book series (LNM, volume 1921)

Table of contents

  1. Front Matter
    Pages I-XI
  2. Pages 1-7
  3. Pages 9-16
  4. Pages 17-52
  5. Back Matter
    Pages 119-129

About this book


Behind genetics and Markov chains, there is an intrinsic algebraic structure. It is defined as a type of new algebra: as evolution algebra. This concept lies between algebras and dynamical systems. Algebraically, evolution algebras are non-associative Banach algebras; dynamically, they represent discrete dynamical systems. Evolution algebras have many connections with other mathematical fields including graph theory, group theory, stochastic processes, dynamical systems, knot theory, 3-manifolds, and the study of the Ihara-Selberg zeta function. In this volume the foundation of evolution algebra theory and applications in non-Mendelian genetics and Markov chains is developed, with pointers to  some further research topics.


Algebraic structure Group theory Lie algebra Probability theory algebra biology genetics theory of evolution

Authors and affiliations

  1. 1.Mathematical Biosciences InstituteThe Ohio State UniversityColumbusUSA
  2. 2.Mathematics DepartmentCollege of William and MaryWilliamsburgUSA

Bibliographic information


From the reviews:

"The book introduces a new class of nonassociative algebras, called evolution algebras, and discusses in detail many applications of evolution algebras in stochastic processes and genetics. … The book under review is suitable both for graduate students and researchers with interest in the theoretical biology, genetics, Markov process, graph theory, and nonassociative algebras and their applications. The text contains a clear, detailed and self-contained exposition of evolution algebras."(Fouad Zitan, Zentralblatt MATH, Vol. 1136 (14), 2008)