Bachelor Project Mathematics: A Hidden Symmetry of Kontsevich's Tetrahedral Flow on the Space of Rescaled 3D and 4D-Determinant Nambu-Poisson Brackets

Lipper, Dimitri (2021) Bachelor Project Mathematics: A Hidden Symmetry of Kontsevich's Tetrahedral Flow on the Space of Rescaled 3D and 4D-Determinant Nambu-Poisson Brackets. Bachelor's Thesis, Mathematics.

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Abstract

We study symmetries of the space of Poisson brackets. Kontsevich's tetrahedral flow is known to preserve the class of 3d and 4d-determinant Nambu-Poisson brackets. This gives rise to dynamical systems contain-ing differential polynomials in the right hand side. These expressions are highly symmetric, and we want to unravel their structure. To solve the problem we design an algorithm and implement it in Maple. We confirm the triple total skew-symmetry of that flow and we discover in which sense the structure of that flow is minimal. Our approach naturally generalizes to higher dimensions and other Kontsevich flows, yet it is unknown whether the minimal structure persists or not.

Item Type:	Thesis (Bachelor's Thesis)
Supervisor name:	Kiselev, A.V.
Degree programme:	Mathematics
Thesis type:	Bachelor's Thesis
Language:	English
Date Deposited:	31 Aug 2021 13:51
Last Modified:	31 Aug 2021 13:51
URI:	https://fse.studenttheses.ub.rug.nl/id/eprint/25827

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