Super Hamiltonian operators and Lie superalgebras (Q750988)

The authors prove that with every linear super Hamiltonian operator one can associate a Lie superalgebra structure on the space of (reduced) 1- forms and vice versa. A theorem is also proved about the connection between 2-cocycles on this Lie superalgebra and super Hamiltonian operators. The paper provides an interesting application to the sKdV equation as well as a superversion of the formal calculus of variations as developed by I. M. Gel'fand et al.