Limit search to available items
Book Cover
Author Aguiar, Marcelo, 1968- author.

Title Bimonoids for hyperplane arrangements / Marcelo Aguiar, Swapneel Mahajan
Published Cambridge ; New York, NY : Cambridge University Press, 2020


Description 1 online resource (xx, 832 pages)
Series Encyclopedia of mathematics and its applications ; 173
Encyclopedia of mathematics and its applications ; v. 173.
Contents Part I. Species and Operads: -- Hyperplane arrangements -- Species and bimonoids -- Bimonads on species -- Operads -- Part II. Basic Theory of Bimonoids: -- Primitive filtrations and decomposable filtrations -- Universal constructions -- Examples of bimonoids -- Hadamard product -- Exponential and logarithm -- Characteristic operations -- Modules over monoid algebras and bimonoids in species -- Antipode -- Part III. Structure Results for Bimonoids: -- Loday-Ronco, Leray-Samelson, Borel-Hopf -- Hoffman-Newman-Radford -- Freeness under Hadamard products -- Lie monoids -- Poincaré-Birkhoff-Witt and Cartier-Milnor-Moore
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, Poincar-̌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
Bibliography Includes bibliographical references and indexes
Notes Online resource; title from digital title page (viewed on April 15, 2020)
Subject Incidence algebras.
Algebraic spaces.
Geometry, Plane.
Variedades algebraicas
Algebraic spaces
Geometry, Plane
Incidence algebras
Form Electronic book
Author Mahajan, Swapneel Arvind, 1974- author.
ISBN 9781108863117