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Bimonoids for Hyperplane Arrangements [slightly glitchy PDF] by Marcelo Aguiar; Swapneel Mahajan; Cambridge University Press is a nonfiction available to read on EtoBox.

What is Bimonoids for Hyperplane Arrangements [slightly glitchy PDF] about?

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 common ground in this theory. The authors introduce notions of monoid, comonoid, bimonoid, and Lie monoid relative to a fixed hyperplane arrangement. Faces, flats, and lunes of the arrangement provide the building blocks for these concepts. They also construct universal bimonoids by using generalizations of the classical notions of shuffle and quasishuf- fle, and establish the Borel–Hopf, Poincaré–Birkhoff–Witt, and Cartier–Milnor– Moore theorems in this new setting. A key role is played by noncommutative zeta and Möbius functions which generalize the classical exponential and logarithm, and by the representation theory of the Tits algebra. 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, s

Who reads Bimonoids for Hyperplane Arrangements [slightly glitchy PDF]?

Author

Marcelo Aguiar; Swapneel Mahajan; Cambridge University Press

Publisher

Cambridge University Press (Virtual Publishing)

Published

2020

Language

EN

ISBN

9781108863117

Category

nonfiction

Subjects

Mathematics, Stem