Evolution Algebras and their Applications

  • Jianjun Paul Tian

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

Introduction

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.

Keywords

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

Authors and affiliations

  • Jianjun Paul Tian
    • 1
    • 2
  1. 1.Mathematical Biosciences InstituteThe Ohio State UniversityColumbusUSA
  2. 2.Mathematics DepartmentCollege of William and MaryWilliamsburgUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-74284-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 2008
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-74283-8
  • Online ISBN 978-3-540-74284-5
  • Series Print ISSN 0075-8434
  • About this book