Show code: [gcaops]

The sea of Poisson Structures and its Graph Complex flows

Index » Nambu–Poisson structure on $\mathbb{R}^4$

Alternative names:
  • Jacobian Poisson Structure (JPS) on $\mathbb{R}^4$
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Definition

Formula:$P = -[[\frac{\partial}{\partial x} \wedge \frac{\partial}{\partial y} \wedge \frac{\partial}{\partial z} \wedge \frac{\partial}{\partial w}, u_1], u_2]$ where $u_1, u_2 \in C^\infty(\mathbb{R}^4)$ are arbitrary.
Code (gcaops):
S.<xi1,xi2,xi3,xi4> = SuperfunctionAlgebra(SR, var('x,y,z,w'), simplify='expand', is_zero='is_trivial_zero')
P = -(xi1*xi2*xi3*xi4).bracket(S(function('u1')(x,y,z,w))).bracket(S(function('u2')(x,y,z,w)))

Deformations

No deformations have been stored in the database so far.