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portada Bimonoids for Hyperplane Arrangements (Encyclopedia of Mathematics and its Applications)
Type
Physical Book
Author
Publisher
Year
2020
Language
English
Pages
824
Format
Hardcover
Dimensions
23.6 x 16.3 x 4.3 cm
Weight
1.45 kg.
ISBN13
9781108495806
Categories

Bimonoids for Hyperplane Arrangements (Encyclopedia of Mathematics and its Applications)

Marcelo Aguiar (Author) · Swapneel Mahajan (Author) · Cambridge University Press · Hardcover

Bimonoids for Hyperplane Arrangements (Encyclopedia of Mathematics and its Applications) - Aguiar, Marcelo ; Mahajan, Swapneel

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Synopsis "Bimonoids for Hyperplane Arrangements (Encyclopedia of Mathematics and its Applications) "

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.

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