Bimonoids for Hyperplane Arrangements

Marcelo Aguiar is Professor in the Department of Mathematics at Cornell University, New York. Swapneel Mahajan is Associate Professor in the Department of Mathematics at the Indian Institute of Technology, Bombay.

• 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.

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