Bimonoids for hyperplane arrangements

by Aguiar, Marcelo

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Title Statements

Full title :Bimonoids for hyperplane arrangements / Marcelo Aguiar (Cornell University, Ithaca), Swapneel Mahajan (Indian Institute of Technology, Bombay).

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.

Edition Statements

Publication Date:2020

Publication Statements

Publisher(s):Cambridge University Press
Place of Publication:Cambridge
Language:eng
Publication Date:2020

The Physical Object

Description:xx, 832 Seiten : Illustrationen : 24 cm

Edition Identifiers

ISBN:9781108495806, 110849580X
oclc:on1192361046
LC Classification:QA251.3
Dewey Decimal:516/.11

Subjects

Algebraic spaces Algèbres d'incidence Espaces algébriques Géométrie plane Geometry, Modern -- Plane Geometry, Plane Hyperespace Hyperspace Incidence algebras