Bimonoids for Hyperplane Arrangements

Bimonoids for Hyperplane Arrangements
Author :
Publisher : Cambridge University Press
Total Pages : 854
Release :
ISBN-10 : 9781108852784
ISBN-13 : 1108852785
Rating : 4/5 (84 Downloads)

Book Synopsis Bimonoids for Hyperplane Arrangements by : Marcelo Aguiar

Download or read book Bimonoids for Hyperplane Arrangements written by Marcelo Aguiar and published by Cambridge University Press. This book was released on 2020-03-19 with total page 854 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


Bimonoids for Hyperplane Arrangements Related Books

Bimonoids for Hyperplane Arrangements
Language: en
Pages: 854
Authors: Marcelo Aguiar
Categories: Mathematics
Type: BOOK - Published: 2020-03-19 - Publisher: Cambridge University Press

DOWNLOAD EBOOK

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
Bimonoids for Hyperplane Arrangements
Language: en
Pages: 853
Authors: Marcelo Aguiar
Categories: Mathematics
Type: BOOK - Published: 2020-03-19 - Publisher: Cambridge University Press

DOWNLOAD EBOOK

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
Coxeter Bialgebras
Language: en
Pages: 897
Authors: Marcelo Aguiar
Categories: Mathematics
Type: BOOK - Published: 2022-10-31 - Publisher: Cambridge University Press

DOWNLOAD EBOOK

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 ge
Quasi-Hopf Algebras
Language: en
Pages: 545
Authors: Daniel Bulacu
Categories: Mathematics
Type: BOOK - Published: 2019-02-21 - Publisher: Cambridge University Press

DOWNLOAD EBOOK

This self-contained book dedicated to Drinfeld's quasi-Hopf algebras takes the reader from the basics to the state of the art.
Basic Category Theory
Language: en
Pages: 193
Authors: Tom Leinster
Categories: Mathematics
Type: BOOK - Published: 2014-07-24 - Publisher: Cambridge University Press

DOWNLOAD EBOOK

A short introduction ideal for students learning category theory for the first time.