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  Simplex and polygon equations

Dimakis, A., & Müller-Hoissen, F. (2015). Simplex and polygon equations. Symmetry, Integrability and Geometry: Methods and Applications, 11: 042. doi:10.3842/SIGMA.2015.042.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0029-0ED1-6 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-002A-AB4B-4
Genre: Journal Article

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 Creators:
Dimakis, Aristophanis, Author
Müller-Hoissen, Folkert1, Author              
Affiliations:
1Max Planck Institute for Dynamics and Self-Organization, Max Planck Society, ou_2063285              

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Free keywords: Higher Bruhat order; higher Tamari order; pentagon equation; simplex equation
 Abstract: 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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Language(s): eng - English
 Dates: 2015-06-05
 Publication Status: Published online
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Method: Peer
 Identifiers: eDoc: 711940
DOI: 10.3842/SIGMA.2015.042
 Degree: -

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Title: Symmetry, Integrability and Geometry: Methods and Applications
  Abbreviation : SIGMA
Source Genre: Journal
 Creator(s):
Affiliations:
Publ. Info: -
Pages: 49 Volume / Issue: 11 Sequence Number: 042 Start / End Page: - Identifier: ISSN: 1815-0659