This book is part of Algebra and Geometry, a subject within the SCIENCES collection published by ISTE and Wiley, and the second of three volumes specifically focusing on algebra and its applications. Algebra and Applications 2 centers on the increasing role played by combinatorial algebra and Hopf algebras, including an overview of the basic theories on non-associative algebras, operads and (combinatorial) Hopf algebras. The chapters are written by recognized experts in the field, providing insight into new trends, as well as a comprehensive introduction to the theory. The book incorporates self-contained surveys with the main results, applications and perspectives.
The chapters in this volume cover a wide variety of algebraic structures and their related topics. Alongside the focal topic of combinatorial algebra and Hopf algebras, non-associative algebraic structures in iterated integrals, chronological calculus, differential equations, numerical methods, control theory, non-commutative symmetric functions, Lie series, descent algebras, Butcher groups, chronological algebras, Magnus expansions and Rota–Baxter algebras are explored.
Algebra and Applications 2 is of great interest to graduate students and researchers. Each chapter combines some of the features of both a graduate level textbook and of research level surveys.
1. Algebraic Background for Numerical Methods, Control Theory and Renormalization, Dominique Manchon.
2. From Iterated Integrals and Chronological Calculus to Hopf and Rota–Baxter Algebras, Kurusch Ebrahimi-Fard and Frédéric Patras.
3. Noncommutative Symmetric Functions, Lie Series and Descent Algebras, Jean-Yves Thibon.
4. From Runge–Kutta Methods to Hopf Algebras of Rooted Trees, Ander Murua.
5. Combinatorial Algebra in Controllability and Optimal Control, Matthias Kawski.
6. Algebra is Geometry is Algebra – Interactions Between Hopf Algebras, Infinite Dimensional Geometry and Application, Alexander Schmeding.
Abdenacer Makhlouf is a Professor and head of the mathematics department at the University of Haute Alsace, France. His research covers structure, representation theory, deformation theory and cohomology of various types of algebras, including non-associative algebras, Hopf algebras and n-ary algebras.
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