On field theoretic generalizations of a Poisson algebra (Q1387175)

A few generalizations of Poisson algebras to field theory canonically formulated in terms of polymomentum variables are discussed. A graded Poisson bracket on differential forms and an \((n+1)\)-ry bracket on functions are considered. The Poisson bracket on differential forms gives rise to various generalizations of Gerstenhaber algebras: noncommutative (in the sense of Loday) and higher-order (in the sense of higher-order graded Leibniz rule).