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Discrete projective polygons and Hamiltonian structures Mari-Beffa, Gloria
Description
Decades ago Semenov-Tian-Shansky defined the so-called twisted Poisson structure on $G^N$, where $G$ is a Poisson Lie group. We will review the definition and show that in the case $G = PSL(n+1)$, it can be reduced to the moduli space of projective polygons (under the projective action), as defined by the discrete projective curvatures. We will also show that any reduced Hamiltonian evolution is induced on the curvatures by a simple polygon evolution that can be defined directly from the variation of the Hamiltonian function. We will also define a second structure reducing a right invariant tensor, which is proven to be compatible with the previous reduction for dimensions 2 and 3, and conjectured to be for any dimension. The pair are Hamiltonian structures for integrable discretizations of W_n algebras in any dimension. Thus, one can write a very simple realization of this integrable system as an evolution of projective polygons. This is joint work with Jing Ping Wang.
Item Metadata
Title |
Discrete projective polygons and Hamiltonian structures
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2016-06-16T12:42
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Description |
Decades ago Semenov-Tian-Shansky defined the so-called twisted Poisson structure on $G^N$, where $G$ is a Poisson Lie group. We will review the definition and show that in the case $G = PSL(n+1)$, it can be reduced to the moduli space of projective polygons (under the projective action), as defined by the discrete projective curvatures. We will also show that any reduced Hamiltonian evolution is induced on the curvatures by a simple polygon evolution that can be defined directly from the variation of the Hamiltonian function. We will also define a second structure reducing a right invariant tensor, which is proven to be compatible with the previous reduction for dimensions 2 and 3, and conjectured to be for any dimension. The pair are Hamiltonian structures for integrable discretizations of W_n algebras in any dimension. Thus, one can write a very simple realization of this integrable system as an evolution of projective polygons. This is joint work with Jing Ping Wang.
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Extent |
38 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: University of Wisconsin
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Series | |
Date Available |
2017-01-29
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0340394
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International