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Algebra and Applications 2 Combinatorial Algebra and Hopf Algebras 1st Edition by Makhlouf Abdenacer ISBN 9781789450187 1789450187

Name: Algebra and Applications 2 Combinatorial Algebra and Hopf Algebras 1st Edition by Makhlouf Abdenacer ISBN 9781789450187 1789450187
SKU: EB-36488550
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Algebra and Applications 2 Combinatorial Algebra and Hopf Algebras 1st Edition Makhlouf Abdenacer Digital Instant Download

Author(s): Makhlouf Abdenacer

Edition: 1

File Details: PDF, 4.03 MB

Year: 2021

Language: english

SKU: EB-36488550 Category: Uncategorized Tag: Makhlouf Abdenacer

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Algebra and Applications 2 Combinatorial Algebra and Hopf Algebras 1st Edition by Makhlouf Abdenacer – Ebook PDF Instant Download/Delivery: 9781789450187 ,1789450187
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ISBN 10: 1789450187
ISBN 13: 9781789450187
Author: Makhlouf Abdenacer

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.

Algebra and Applications 2 Combinatorial Algebra and Hopf Algebras 1st Edition Table of contents:

1 Algebraic Background for Numerical Methods, Control Theory and Renormalization

1.1. Introduction

1.2. Hopf algebras: general properties

1.3. Connected Hopf algebras

1.4. Pre-Lie algebras

1.5. Algebraic operads

1.6. Pre-Lie algebras (continued)

1.7. Other related algebraic structures

1.8. References

2 From Iterated Integrals and Chronological Calculus to Hopf and Rota–Baxter Algebras

2.1. Introduction

2.2. Generalized iterated integrals

2.3. Advances in chronological calculus

2.4. Rota–Baxter algebras

2.5. References

3 Noncommutative Symmetric Functions, Lie Series and Descent Algebras

3.1. Introduction

3.2. Classical symmetric functions

3.3. Noncommutative symmetric functions

3.4. Lie series and Lie idempotents

3.5. Lie idempotents as noncommutative symmetric functions

3.6. Decompositions of the descent algebras

3.7. Decompositions of the tensor algebra

3.8. General deformations

3.9. Lie quasi-idempotents as Lie polynomials

3.10. Permutations and free quasi-symmetric functions

3.11. Packed words and word quasi-symmetric functions

3.12. References

4 From Runge–Kutta Methods to Hopf Algebras of Rooted Trees

4.1. Numerical integration methods for ordinary differential equations

4.2. Algebraic theory of Runge–Kutta methods

4.3. B-series and related formal expansions

4.4. Hopf algebras of rooted trees

4.5. References

5 Combinatorial Algebra in Controllability and Optimal Control

5.1. Introduction

5.2. Analytic foundations

5.3. Controllability and optimality

5.4. Product expansions and realizations

5.5. References

6 Algebra is Geometry is Algebra – Interactions Between Hopf Algebras, Infinite Dimensional Geometry and Application

6.1. The Butcher group and the Connes–Kreimer algebra

6.2. Character groups of graded and connected Hopf algebras

6.3. Controlled groups of characters

6.4. Appendix: Calculus in locally convex spaces

6.5. References

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Tags: Makhlouf Abdenacer, Applications, Combinatorial Algebra, Hopf Algebras