Evolution Algebras and Their Applications

Jianjun Paul Tian (auth.)3540742832, 978-3-540-74283-8

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.

Table of contents :
Front Matter….Pages I-XI
Introduction….Pages 1-7
Motivations….Pages 9-16
Evolution Algebras….Pages 17-52
Evolution Algebras and Markov Chains….Pages 53-90
Evolution Algebras and Non-Mendelian Genetics….Pages 91-107
Further Results and Research Topics….Pages 109-118
Back Matter….Pages 119-129