| 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 |
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| 050 | 4 |
_aQA251.3 _b.A357 2020 |
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| 082 | 0 | 4 |
_a516/.11 _223 |
| 100 | 1 |
_aAguiar, Marcelo, _d1968- _eauthor. |
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| 245 | 1 | 0 |
_aBimonoids for hyperplane arrangements / _cMarcelo Aguiar, Swapneel Mahajan. |
| 264 | 1 |
_aCambridge : _bCambridge University Press, _c2020. |
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| 300 |
_a1 online resource (xx, 832 pages) : _bdigital, PDF file(s). |
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| 336 |
_atext _btxt _2rdacontent |
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| 337 |
_acomputer _bc _2rdamedia |
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| 338 |
_aonline resource _bcr _2rdacarrier |
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| 490 | 1 |
_aEncyclopedia of mathematics and its applications ; _v173 |
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| 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. |
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| 776 | 0 | 8 |
_iPrint version: _z9781108495806 |
| 830 | 0 |
_aEncyclopedia of mathematics and its applications ; _v173. |
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| 856 | 4 | 0 | _uhttps://doi.org/10.1017/9781108863117 |
| 999 |
_c529001 _d528999 |
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