The Resource Bimonoids for hyperplane arrangements, Marcelo Aguiar, Swapneel Mahajan, (electronic resource)
Bimonoids for hyperplane arrangements, Marcelo Aguiar, Swapneel Mahajan, (electronic resource)
Resource Information
The item Bimonoids for hyperplane arrangements, Marcelo Aguiar, Swapneel Mahajan, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Bowdoin College Library.This item is available to borrow from 1 library branch.
Resource Information
The item Bimonoids for hyperplane arrangements, Marcelo Aguiar, Swapneel Mahajan, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Bowdoin College Library.
This item is available to borrow from 1 library branch.
- 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, 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
- Language
- eng
- Extent
- 1 online resource (xx, 832 pages)
- Note
- Title from publisher's bibliographic system (viewed on 28 Feb 2020)
- Isbn
- 9781108863117
- Label
- Bimonoids for hyperplane arrangements
- Title
- Bimonoids for hyperplane arrangements
- Statement of responsibility
- Marcelo Aguiar, Swapneel Mahajan
- Language
- eng
- 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, 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
- Cataloging source
- UkCbUP
- http://library.link/vocab/creatorDate
- 1968-
- http://library.link/vocab/creatorName
- Aguiar, Marcelo
- Index
- index present
- Literary form
- non fiction
- Nature of contents
- dictionaries
- http://library.link/vocab/relatedWorkOrContributorDate
- 1974-
- http://library.link/vocab/relatedWorkOrContributorName
- Mahajan, Swapneel Arvind
- Series statement
- Encyclopedia of mathematics and its applications
- Series volume
- 173
- http://library.link/vocab/subjectName
-
- Incidence algebras
- Algebraic spaces
- Hyperspace
- Geometry, Plane
- Label
- Bimonoids for hyperplane arrangements, Marcelo Aguiar, Swapneel Mahajan, (electronic resource)
- Note
- Title from publisher's bibliographic system (viewed on 28 Feb 2020)
- Control code
- ssj0002560782
- Dimensions
- unknown
- Extent
- 1 online resource (xx, 832 pages)
- Form of item
- online
- Governing access note
- Access restricted to subscribing institutions
- Isbn
- 9781108863117
- Isbn Type
- (ebook)
- Other physical details
- digital, PDF file(s)
- Specific material designation
- remote
- System control number
- (WaSeSS)ssj0002560782
- Label
- Bimonoids for hyperplane arrangements, Marcelo Aguiar, Swapneel Mahajan, (electronic resource)
- Note
- Title from publisher's bibliographic system (viewed on 28 Feb 2020)
- Control code
- ssj0002560782
- Dimensions
- unknown
- Extent
- 1 online resource (xx, 832 pages)
- Form of item
- online
- Governing access note
- Access restricted to subscribing institutions
- Isbn
- 9781108863117
- Isbn Type
- (ebook)
- Other physical details
- digital, PDF file(s)
- Specific material designation
- remote
- System control number
- (WaSeSS)ssj0002560782
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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.bowdoin.edu/portal/Bimonoids-for-hyperplane-arrangements-Marcelo/I0Z8ss8sSaU/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.bowdoin.edu/portal/Bimonoids-for-hyperplane-arrangements-Marcelo/I0Z8ss8sSaU/">Bimonoids for hyperplane arrangements, Marcelo Aguiar, Swapneel Mahajan, (electronic resource)</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.bowdoin.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="https://link.bowdoin.edu/">Bowdoin College Library</a></span></span></span></span></div>
