Simplex and Polygon Equations
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Simplex and Polygon Equations
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| Creator |
Dimakis, A.
Müller-Hoissen, F. |
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| Description |
It is shown that higher Bruhat orders admit a decomposition into a higher Tamari order, the corresponding dual Tamari order, and a ''mixed order''. We describe simplex equations (including the Yang-Baxter equation) as realizations of higher Bruhat orders. Correspondingly, a family of ''polygon equations'' realizes higher Tamari orders. They generalize the well-known pentagon equation. The structure of simplex and polygon equations is visualized in terms of deformations of maximal chains in posets forming 1-skeletons of polyhedra. The decomposition of higher Bruhat orders induces a reduction of the N-simplex equation to the (N+1)-gon equation, its dual, and a compatibility equation.
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| Date |
2019-02-13T16:25:31Z
2019-02-13T16:25:31Z 2015 |
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| Type |
Article
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| Identifier |
Simplex and Polygon Equations / A. Dimakis, F. Müller-Hoissen // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 107 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 06A06; 06A07; 52Bxx; 82B23 DOI:10.3842/SIGMA.2015.042 http://dspace.nbuv.gov.ua/handle/123456789/147105 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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