Higher Courant-Dorfman algebras and associated higher Poisson vertex algebras
arXiv:2302.11420 · doi:10.1016/j.geomphys.2026.105870
Abstract
In this paper, we consider a notion of a higher version of the relation between Courant-Dorfman algebras and Poisson vertex algebras. We define a higher Courant-Dorfman algebra, and study the relationship with graded symplectic geometry. In particular, we give graded Poisson algebras of degree in the non-degenerate case. For higher Courant-Dorfman algebras coming from finite-dimensional vector bundles, they coincide with the algebras of functions of the associated differential-graded(dg) symplectic manifolds of degree . We define a higher Lie conformal algebra and Poisson vertex algebra, and give a higher (weak) Courant-Dorfman algebraic structure arising from them. Moreover, we prove that the higher Lie conformal algebras and higher Poisson vertex algebras have properties like Lie conformal algebras and Poisson vertex algebras. As an example, we obtain an algebraic description of Batalin-Fradkin-Vilkovisky(BFV) current algebras.
28 pages, significantly revised