TY  - BOOK
AU  - Aguiar,Marcelo
AU  - Mahajan,Swapneel Arvind
TI  - Bimonoids for hyperplane arrangements
T2  - Encyclopedia of mathematics and its applications
SN  - 9781108863117 (ebook)
AV  - QA251.3 .A357 2020
U1  - 516/.11 23
PY  - 2020///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Incidence algebras
KW  - Algebraic spaces
KW  - Hyperspace
KW  - Geometry, Plane
N1  - Title from publisher's bibliographic system (viewed on 28 Feb 2020)
N2  - 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
UR  - https://doi.org/10.1017/9781108863117
ER  -