| Bimonoids for Hyperplane Arrangements Contributor(s): Aguiar, Marcelo (Author), Mahajan, Swapneel (Author) |
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ISBN: 110849580X ISBN-13: 9781108495806 Publisher: Cambridge University Press OUR PRICE: $209.00 Product Type: Hardcover - Other Formats Published: April 2020 |
| Additional Information |
| BISAC Categories: - Mathematics | Discrete Mathematics |
| Series: Encyclopedia of Mathematics and Its Applications |
| Physical Information: 1.7" H x 6.4" W x 9.3" (3.20 lbs) 824 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |
Contributor Bio(s): Aguiar, Marcelo: - Marcelo Aguiar is Professor in the Department of Mathematics at Cornell University, New York.Mahajan, Swapneel: - Swapneel Mahajan is Associate Professor in the Department of Mathematics at the Indian Institute of Technology, Bombay. |