In this on-going work, we study p-brane dynamics from the viewpoint of multisymplectic geometry, in which the standard symplectic 2-form is replaced by a closed non-degenerate (p+2)-form on a finite-dimensional extended phase space. In this setting, graded Poisson brackets organize into an L∞-algebra, providing a higher algebraic framework for brane observables that goes beyond the standard Lie algebraic description. I will show that Poincaré invariance together with the existence of Hamiltonian flows strongly constrains the admissible mass-shell conditions within this framework, recovering the Nambu–Goto constraint as a particular case. I will also discuss multi-coadjoint orbit constructions that parallel the classical orbit method for particles.
