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- W2911598530 abstract "We construct a family of Poisson structures of hydrodynamic type on the loop space of $mathbb{C} P^{n-1}$. This family is parametrized by the moduli space of elliptic curves or, in other words, by the modular parameter $tau$. This family can be lifted to a homogeneous Poisson structure on the loop space of $mathbb{C}^n$ but in order to do that we need to upgrade the modular parameter $tau$ to an additional field $tau(x)$ with Poisson brackets ${tau(x),tau(y)}=0,~~{tau(x),z_a(y)}=2pi i~ z_a(y)~delta^{prime}(x-y)$ where $z_1,...,z_n$ are coordinates on $mathbb{C}^n$. These homogeneous Poisson structures can be written in terms of an elliptic $r$-matrix of hydrodynamic type." @default.
- W2911598530 created "2019-02-21" @default.
- W2911598530 creator A5044104881 @default.
- W2911598530 date "2019-06-01" @default.
- W2911598530 modified "2023-10-18" @default.
- W2911598530 title "Poisson structures on loop spaces of <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline overflow=scroll id=d1e19 altimg=si10.gif><mml:mi>ℂ</mml:mi><mml:msup><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:math> and an <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline overflow=scroll id=d1e31 altimg=si11.gif><mml:mi>r</mml:mi></mml:math>-matrix associated with the universal elliptic curve" @default.
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- W2911598530 doi "https://doi.org/10.1016/j.geomphys.2019.02.012" @default.
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