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Bimonoids for Hyperplane Arrangements on Hardback by Marcelo Aguiar
Bimonoids for Hyperplane Arrangements on Hardback by Marcelo Aguiar
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Bimonoids for Hyperplane Arrangements

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Description

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.

Author Biography:

Marcelo Aguiar is Professor in the Department of Mathematics at Cornell University, New York. Swapneel Mahajan is Associate Professor in the Department of Mathematics at the Indian Institute of Technology, Bombay.
Release date NZ
March 19th, 2020
Pages
824
Audience
  • Postgraduate, Research & Scholarly
Illustrations
Worked examples or Exercises; 30 Tables, black and white; 4 Halftones, color; 6 Halftones, black and white; 3 Line drawings, color; 53 Line drawings, black and white
Dimensions
160x240x42
ISBN-13
9781108495806
Product ID
31787362

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