Grassmannian-parameterized solutions to direct-sum polygon and simplex equations
| Autor: | Aristophanes Dimakis, Igor G. Korepanov |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Simplex
Direct sum 010102 general mathematics Structure (category theory) FOS: Physical sciences Parameterized complexity Statistical and Nonlinear Physics Mathematical Physics (math-ph) Computer Science::Computational Geometry 01 natural sciences Combinatorics Pentagon 15A24 (Primary) 15A75 (Secondary) Grassmannian 0103 physical sciences Polygon Mathematics - Quantum Algebra FOS: Mathematics Quantum Algebra (math.QA) Mathematics::Metric Geometry 010307 mathematical physics 0101 mathematics Mathematical Physics Mathematics Vector space |
| Popis: | We consider polygon and simplex equations, of which the simplest nontrivial examples are pentagon (5-gon) and Yang--Baxter (2-simplex), respectively. We examine the general structure of (2n+1)-gon and 2n-simplex equations in direct sums of vector spaces. Then we provide a construction for their solutions, parameterized by elements of the Grassmannian Gr(n+1,2n+1). 26 pages, 5 tikz figures. v4: Introduction re-written, Discussion added in the end |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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