Evolution Algebras and Their Applications

✍ Scribed by Jianjun Paul Tian (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2008
• Tongue: English
• Leaves: 135
• Series: Lecture notes in mathematics 1921
• Edition: 1
• Category: Library

✦ Synopsis

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

✦ Subjects

General Algebraic Systems; Non-associative Rings and Algebras; Probability Theory and Stochastic Processes; Mathematical Biology in General