Bimonoids for Hyperplane Arrangements

ISBN-13: 9781108495806 / Angielski / Twarda / 2020 / 824 str.

Marcelo Aguiar; Swapneel Mahajan

Opis

Develops a new theory, parallel to the classical theory of connected Hopf algebras, including a real hyperplane arrangement.

Spis treści

Introduction; Part I. Species and Operads: 1. Hyperplane arrangements; 2. Species and bimonoids; 3. Bimonads on species; 4. Operads; Part II. Basic Theory of Bimonoids: 5. Primitive filtrations and decomposable filtrations; 6. Universal constructions; 7. Examples of bimonoids; 8. Hadamard product; 9. Exponential and logarithm; 10. Characteristic operations; 11. Modules over monoid algebras and bimonoids in species; 12. Antipode; Part III. Structure Results for Bimonoids: 13. Loday–Ronco, Leray–Samelson, Borel–Hopf; 14. Hoffman–Newman–Radford; 15. Freeness under Hadamard products; 16. Lie monoids; 17. Poincaré–Birkhoff–Witt and Cartier–Milnor–Moore; Appendix A. Linear algebra; Appendix B. Higher monads; Appendix C. Internal hom; Appendix D. Semidirect products; References; Notation index; Author index; Subject index.