Algebra and Applications 2 Combinatorial Algebra and Hopf Algebras.

Detalles Bibliográficos
Autor principal: Makhlouf, Abdenacer
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Newark : John Wiley & Sons, Incorporated, 2022.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover
  • Half-Title Page
  • Title Page
  • Copyright Page
  • Contents
  • Preface
  • 1. Algebraic Background for Numerical Methods, Control Theory and Renormalization
  • 1.1. Introduction
  • 1.2. Hopf algebras: general properties
  • 1.2.1. Algebras
  • 1.2.2. Coalgebras
  • 1.2.3. Convolution product
  • 1.2.4. Bialgebras and Hopf algebras
  • 1.2.5. Some simple examples of Hopf algebras
  • 1.2.6. Some basic properties of Hopf algebras
  • 1.3. Connected Hopf algebras
  • 1.3.1. Connected graded bialgebras
  • 1.3.2. An example: the Hopf algebra of decorated rooted trees
  • 1.3.3. Connected filtered bialgebras
  • 1.3.4. The convolution product
  • 1.3.5. Characters
  • 1.3.6. Group schemes and the Cartier-Milnor-Moore-Quillen theorem
  • 1.3.7. Renormalization in connected filtered Hopf algebras
  • 1.4. Pre-Lie algebras
  • 1.4.1. Definition and general properties
  • 1.4.2. The group of formal flows
  • 1.4.3. The pre-Lie Poincaré-Birkhoff-Witt theorem
  • 1.5. Algebraic operads
  • 1.5.1. Manipulating algebraic operations
  • 1.5.2. The operad of multi-linear operations
  • 1.5.3. A definition for linear operads
  • 1.5.4. A few examples of operads
  • 1.6. Pre-Lie algebras (continued)
  • 1.6.1. Pre-Lie algebras and augmented operads
  • 1.6.2. A pedestrian approach to free pre-Lie algebra
  • 1.6.3. Right-sided commutative Hopf algebras and the Loday-Ronco theorem
  • 1.6.4. Pre-Lie algebras of vector fields
  • 1.6.5. B-series, composition and substitution
  • 1.7. Other related algebraic structures
  • 1.7.1. NAP algebras
  • 1.7.2. Novikov algebras
  • 1.7.3. Assosymmetric algebras
  • 1.7.4. Dendriform algebras
  • 1.7.5. Post-Lie algebras
  • 1.8. References
  • 2. From Iterated Integrals and Chronological Calculus to Hopf and Rota-Baxter Algebras
  • 2.1. Introduction
  • 2.2. Generalized iterated integrals
  • 2.2.1. Permutations and simplices
  • 2.2.2. Descents, NCSF and the BCH formula
  • 2.2.3. Rooted trees and nonlinear differential equations
  • 2.2.4. Flows and Hopf algebraic structures
  • 2.3. Advances in chronological calculus
  • 2.3.1. Chronological calculus and half-shuffles
  • 2.3.2. Chronological calculus and pre-Lie products
  • 2.3.3. Time-ordered products and enveloping algebras
  • 2.3.4. Formal flows and Hopf algebraic structures
  • 2.4. Rota-Baxter algebras
  • 2.4.1. Origin
  • 2.4.2. Definition and examples

Ejemplares similares