Bimonoids for hyperplane arrangements

著者

• Aguiar, Marcelo
• Mahajan, Swapneel Arvind

書誌事項

Bimonoids for hyperplane arrangements

Marcelo Aguiar, Swapneel Mahajan

（Encyclopedia of mathematics and its applications / edited by G.-C. Rota, 173）

Cambridge University Press, 2020

• : hardback

注記

Includes bibliographical references (p. 763-801) and indexes

内容説明・目次

内容説明

The goal of this monograph is to develop Hopf theory in a new setting which features centrally a real hyperplane arrangement. The new theory is parallel to the classical theory of connected Hopf algebras, and relates to it when specialized to the braid arrangement. Joyal's theory of combinatorial species, ideas from Tits' theory of buildings, and Rota's work on incidence algebras inspire and find a common expression in this theory. The authors introduce notions of monoid, comonoid, bimonoid, and Lie monoid relative to a fixed hyperplane arrangement. They also construct universal bimonoids by using generalizations of the classical notions of shuffle and quasishuffle, and establish the Borel-Hopf, Poincare-Birkhoff-Witt, and Cartier-Milnor-Moore theorems in this setting. This monograph opens a vast new area of research. It will be of interest to students and researchers working in the areas of hyperplane arrangements, semigroup theory, Hopf algebras, algebraic Lie theory, operads, and category theory.

目次

• 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. Poincare-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.

「Nielsen BookData」 より

詳細情報

• NII書誌ID(NCID): BB30033076
• ISBN:
  • 9781108495806
• 出版国コード: uk
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Cambridge
• ページ数/冊数: xx, 832 p.
• 大きさ: 25 cm
• 分類:
  • DC23 : 512.55
• 件名:
  • LCSH : Hopf algebras
  • LCSH : Monoids
  • LCSH : Geometry, Plane
• 親書誌ID:
  • BA00064663