Bimonoids for hyperplane arrangements:
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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| Hauptverfasser: | , |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, United Kingdom ; New York, NY, USA ; Port Melbourne, VIC, Australia ; New Delhi, India ; Singapore
Cambridge University Press
2020
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications
173 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 TUM01 TUM02 UBA01 Volltext |
| Zusammenfassung: | 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 |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 28 Feb 2020) |
| Beschreibung: | 1 Online-Ressource |
| ISBN: | 9781108863117 |
| DOI: | 10.1017/9781108863117 |
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Datensatz im Suchindex
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| author | Aguiar, Marcelo 1968- Mahajan, Swapneel 1974- |
| author_GND | (DE-588)143265873 (DE-588)143265970 |
| author_facet | Aguiar, Marcelo 1968- Mahajan, Swapneel 1974- |
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| dewey-full | 516/.11 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516/.11 |
| dewey-search | 516/.11 |
| dewey-sort | 3516 211 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/9781108863117 |
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| indexdate | 2024-07-10T08:44:56Z |
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| isbn | 9781108863117 |
| language | English |
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| spelling | Aguiar, Marcelo 1968- Verfasser (DE-588)143265873 aut Bimonoids for hyperplane arrangements Marcelo Aguiar (Cornell University, Ithaca), Swapneel Mahajan (Indian Institute of Technology, Mumbai) Cambridge, United Kingdom ; New York, NY, USA ; Port Melbourne, VIC, Australia ; New Delhi, India ; Singapore Cambridge University Press 2020 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Encyclopedia of mathematics and its applications 173 Title from publisher's bibliographic system (viewed on 28 Feb 2020) 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 Incidence algebras Algebraic spaces Hyperspace Geometry, Plane Monoidale Kategorie (DE-588)4170466-6 gnd rswk-swf Hyperebene (DE-588)4161050-7 gnd rswk-swf Hopf-Algebra (DE-588)4160646-2 gnd rswk-swf Hyperebene (DE-588)4161050-7 s Hopf-Algebra (DE-588)4160646-2 s Monoidale Kategorie (DE-588)4170466-6 s DE-604 Mahajan, Swapneel 1974- Verfasser (DE-588)143265970 aut Erscheint auch als Druck-Ausgabe, Hardcover 978-1-108-49580-6 Encyclopedia of mathematics and its applications 173 (DE-604)BV044777929 173 https://doi.org/10.1017/9781108863117 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Aguiar, Marcelo 1968- Mahajan, Swapneel 1974- Bimonoids for hyperplane arrangements Encyclopedia of mathematics and its applications Incidence algebras Algebraic spaces Hyperspace Geometry, Plane Monoidale Kategorie (DE-588)4170466-6 gnd Hyperebene (DE-588)4161050-7 gnd Hopf-Algebra (DE-588)4160646-2 gnd |
| subject_GND | (DE-588)4170466-6 (DE-588)4161050-7 (DE-588)4160646-2 |
| title | Bimonoids for hyperplane arrangements |
| title_auth | Bimonoids for hyperplane arrangements |
| title_exact_search | Bimonoids for hyperplane arrangements |
| title_full | Bimonoids for hyperplane arrangements Marcelo Aguiar (Cornell University, Ithaca), Swapneel Mahajan (Indian Institute of Technology, Mumbai) |
| title_fullStr | Bimonoids for hyperplane arrangements Marcelo Aguiar (Cornell University, Ithaca), Swapneel Mahajan (Indian Institute of Technology, Mumbai) |
| title_full_unstemmed | Bimonoids for hyperplane arrangements Marcelo Aguiar (Cornell University, Ithaca), Swapneel Mahajan (Indian Institute of Technology, Mumbai) |
| title_short | Bimonoids for hyperplane arrangements |
| title_sort | bimonoids for hyperplane arrangements |
| topic | Incidence algebras Algebraic spaces Hyperspace Geometry, Plane Monoidale Kategorie (DE-588)4170466-6 gnd Hyperebene (DE-588)4161050-7 gnd Hopf-Algebra (DE-588)4160646-2 gnd |
| topic_facet | Incidence algebras Algebraic spaces Hyperspace Geometry, Plane Monoidale Kategorie Hyperebene Hopf-Algebra |
| url | https://doi.org/10.1017/9781108863117 |
| volume_link | (DE-604)BV044777929 |
| work_keys_str_mv | AT aguiarmarcelo bimonoidsforhyperplanearrangements AT mahajanswapneel bimonoidsforhyperplanearrangements |