Analogs of the Orthogonal, Hamiltonian, Poisson, and Contact Lie Superalgebras in Characteristic 2

Abstract

Over algebraically closed fields of characteristic 2, the analogs of the orthogonal, symplectic, Hamiltonian, Poisson, and contact Lie superalgebras are described. The number of non-isomorphic types, and several properties of these algebras are unexpected, for example, interpretation in terms of exterior differential forms preserved is not applicable to one of these types. The divided powers of differential forms and related (co)homology are introduced.