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:  LodayRonco, LeraySamelson, BorelHopf  HoffmanNewmanRadford  Freeness under Hadamard products  Lie monoids  PoincaréBirkhoffWitt and CartierMilnorMoore 
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 BorelHopf, PoincařBirkhoffWitt, and CartierMilnorMoore 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.


Hyperspace.


Geometry, Plane.


Hiperespacio


Variedades algebraicas


Algebraic spaces


Geometry, Plane


Hyperspace


Incidence algebras

Form 
Electronic book

Author 
Mahajan, Swapneel Arvind, 1974 author.

ISBN 
9781108863117 

1108863116 

9781108852784 

1108852785 
