Bimonoids for Hyperplane Arrangements - Aguiar, Marcelo

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Résumé :
Suitable for graduate students and researchers in diverse areas of mathematics, this monograph offers a new perspective on the classical theory of connected Hopf algebras, and extends it to a new setting where a real hyperplane arrangement is a central feature.

Biographie:
Marcelo Aguiar is Professor in the Department of Mathematics at Cornell University, New York.

Sommaire:
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. Poincar??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.