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Coxeter Bialgebras

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Coxeter Bialgebras

Coxeter Bialgebras

Marcelo Aguiar, Cornell University, Ithaca
Swapneel Mahajan, Indian Institute of Technology, Mumbai
November 2022
Available
Hardback
9781009243773
AUD$251.95
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    Description

    The goal of this monograph is to develop Hopf theory in the setting of a real reflection arrangement. The central notion is that of a Coxeter bialgebra which generalizes the classical notion of a connected graded Hopf algebra. The authors also introduce the more structured notion of a Coxeter bimonoid and connect the two notions via a family of functors called Fock functors. These generalize similar functors connecting Hopf monoids in the category of Joyal species and connected graded Hopf algebras. This monograph opens a new chapter in Coxeter theory as well as in Hopf theory, connecting the two. It also relates fruitfully to many other areas of mathematics such as discrete geometry, semigroup theory, associative algebras, algebraic Lie theory, operads, and category theory. It is carefully written, with effective use of tables, diagrams, pictures, and summaries. It will be of interest to students and researchers alike.

    • Readers get to learn a theory first hand from its original creators
    • Carefully designed chapters, with effective use of tables, diagrams, summaries, worked examples, and exercises with hints
    • Touches many different areas of mathematics with minimum prerequisites so readers can choose entry points depending on their background and interest
    • Suitable for use as a course textbook, or to run a seminar, or for self-study

    Product details

    November 2022
    Hardback
    9781009243773
    894 pages
    241 × 160 × 46 mm
    1.59kg
    Available

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    Contents

    Table of Contents

    • Introduction
    • 1. Coxeter groups and reflection arrangements
    • Part I. Coxeter Species:
    • 2. Coxeter species and Coxeter bimonoids
    • 3. Basic theory of Coxeter bimonoids
    • 4. Examples of Coxeter bimonoids
    • 5. Coxeter operads
    • 6. Coxeter Lie monoids
    • 7. Structure theory of Coxeter bimonoids
    • Part II. Coxeter Spaces:
    • 8. Coxeter spaces and Coxeter bialgebras
    • 9. Basic theory of Coxeter bialgebras
    • 10. Examples of Coxeter bialgebras
    • 11. Coxeter operad algebras
    • 12. Coxeter Lie algebras
    • 13. Structure theory of Coxeter bialgebras
    • Part III. Fock Functors:
    • 14. Fock functors
    • 15. Coxeter bimonoids and Coxeter bialgebras
    • 16. Adjoints of Fock functors
    • 17. Structure theory under Fock functors
    • 18. Examples of Fock spaces
    • Appendix A. Category theory
    • References
    • List of Notations
    • List of Tables
    • List of Figures
    • List of Summaries
    • Author Index
    • Subject Index.
      • Show more

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    About the authors
      Authors
    • Marcelo Aguiar , Cornell University, Ithaca

      Marcelo Aguiar is Professor in the Department of Mathematics at Cornell University, Ithaca.

    • Swapneel Mahajan , Indian Institute of Technology, Mumbai

      Swapneel Mahajan is Associate Professor in the Department of Mathematics at the Indian Institute of Technology, Mumbai.

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