Bimonoids for hyperplane arrangements

Resource Information

The work Bimonoids for hyperplane arrangements represents a distinct intellectual or artistic creation found in Bowdoin College Library. This resource is a combination of several types including: Work, Language Material, Books.

Label

Bimonoids for hyperplane arrangements

Statement of responsibility

Marcelo Aguiar, Swapneel Mahajan

Creator

• Aguiar, Marcelo, 1968-

Contributor

• Mahajan, Swapneel Arvind, 1974-

Subject

• Geometry, Plane
• Hyperspace
• Algebraic spaces
• Incidence algebras

Language

eng

Summary

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, Poincaré-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

Member of

• Encyclopedia of mathematics and its applications, 173

Cataloging source

UkCbUP

Index

index present

Literary form

non fiction

Nature of contents

dictionaries

Series statement

Encyclopedia of mathematics and its applications

Series volume

173