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          Institute: MPI für Dynamik und Selbstorganisation     Collection: Dynamik komplexer Fluide     Display Documents



ID: 711940.0, MPI für Dynamik und Selbstorganisation / Dynamik komplexer Fluide
Simplex and polygon equations
Authors:Dimakis, Aristophanis; Müller-Hoissen, Folkert
Language:English
Date of Publication (YYYY-MM-DD):2015-06-05
Title of Journal:Symmetry, Integrability and Geometry: Methods and Applications
Journal Abbrev.:SIGMA
Volume:11
Sequence Number of Article:042
Review Status:Peer-review
Audience:Experts Only
Abstract / 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.
External Publication Status:published
Document Type:Article
Communicated by:Folkert Müller-Hoissen
Affiliations:MPI für Dynamik und Selbstorganisation/Dynamik komplexer Fluide
External Affiliations:Department of Financial and Management Engineering, University of the Aegean, Chios, Greece
Identifiers:DOI:10.3842/SIGMA.2015.042
URL:http://www.emis.de/journals/SIGMA/2015/042
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