000 02383nam a22003858i 4500
001 CR9781108863117
003 UkCbUP
005 20200416205201.0
006 m|||||o||d||||||||
007 cr||||||||||||
008 190814s2020||||enk o ||1 0|eng|d
020 _a9781108863117 (ebook)
020 _z9781108495806 (hardback)
040 _aUkCbUP
_beng
_erda
_cUkCbUP
050 4 _aQA251.3
_b.A357 2020
082 0 4 _a516/.11
_223
100 1 _aAguiar, Marcelo,
_d1968-
_eauthor.
245 1 0 _aBimonoids for hyperplane arrangements /
_cMarcelo Aguiar, Swapneel Mahajan.
264 1 _aCambridge :
_bCambridge University Press,
_c2020.
300 _a1 online resource (xx, 832 pages) :
_bdigital, PDF file(s).
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
490 1 _aEncyclopedia of mathematics and its applications ;
_v173
500 _aTitle from publisher's bibliographic system (viewed on 28 Feb 2020).
520 _aThe 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.
650 0 _aIncidence algebras.
650 0 _aAlgebraic spaces.
650 0 _aHyperspace.
650 0 _aGeometry, Plane.
700 1 _aMahajan, Swapneel Arvind,
_d1974-
_eauthor.
776 0 8 _iPrint version:
_z9781108495806
830 0 _aEncyclopedia of mathematics and its applications ;
_v173.
856 4 0 _uhttps://doi.org/10.1017/9781108863117
999 _c529001
_d528999