Swapping algebra, Virasoro algebra and discrete integrable system

2014/12/14 by Zhe Sun, Sun, Zhe
Chemistry · Mathematics · Physics and Astronomy · #05E99 #53D30 #Algebraic structures and combinatorial models #Combinatorics (math.CO) #Differential Geometry (math.DG) #FOS: Mathematics #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1412.4330

openalex publication_date 2014/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We induce a Poisson algebra \⋅,⋅\_C_n,N on the configuration space C_n,N of N twisted polygons in \mathbbRP^n-1 from the swapping algebra \citeL12, which is found coincide with Faddeev-Takhtajan-Volkov algebra for n=2. There is another Poisson algebra \⋅,⋅\_S2 on C_2,N induced from the first Adler-Gelfand-Dickey Poissson algebra by Miura transformation. By observing that these two Poisson algebras are asymptotically related to the dual to the Virasoro algebra, finally, we prove that \⋅,⋅\_C_2,N and \⋅,⋅\_S2 are Schouten commute.

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