Bimonoids for hyperplane arrangements /

Bimonoids for hyperplane arrangements /

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Bibliographic Details
Author / Creator:	Aguiar, Marcelo, 1968- author.
Imprint:	Cambridge, United Kingdom ; New York, NY, United States : Cambridge University Press, 2020. ©2020
Description:	xx, 832 pages : illustrations ; 24 cm
Language:	English
Series:	Encyclopedia of mathematics and its applications ; 173 Encyclopedia of mathematics and its applications ; 173. Encyclopedia of mathematics and its applications ; v. 173.
Subject:	Hopf algebras. Incidence algebras. Algebraic spaces. Monoids. Geometry, Plane. Geometry, Plane. Hopf algebras. Monoids.
Format:	Print Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/12357381

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Other authors / contributors:	Mahajan, Swapneel Arvind, 1974- author.
ISBN:	9781108495806 110849580X 9781108863117 1108863116 9781108852784 1108852785
Notes:	Includes bibliographical references (pages 763-801) and index.
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." --

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Call Number:	QA613.8.A3854 2020
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