Bimonoids for hyperplane arrangements / Marcelo Aguiar, Swapneel Mahajan.
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 combinatori...
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| Online Access: |
Full Text (via Cambridge) |
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| Main Authors: | , |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge ; New York, NY :
Cambridge University Press,
2020.
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| Series: | Encyclopedia of mathematics and its applications ;
v. 173. |
| Subjects: |
| 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. |
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| Physical Description: | 1 online resource (xx, 832 pages) |
| Bibliography: | Includes bibliographical references and indexes. |
| ISBN: | 9781108863117 1108863116 9781108852784 1108852785 |
| DOI: | 10.1017/9781108863117 |
| Source of Description, Etc. Note: | Online resource; title from digital title page (viewed on April 15, 2020). |