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 BorelHopf, PoincaréBirkhoffWitt, and CartierMilnorMoore 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 BorelHopf, PoincaréBirkhoffWitt, and CartierMilnorMoore 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 faexternallinksquare fafw"></i> Data from <span resource="http://link.bowdoin.edu/portal/BimonoidsforhyperplanearrangementsMarcelo/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/BimonoidsforhyperplanearrangementsMarcelo/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>