Odd Hamiltonian superalgebras and special odd Hamiltonian superalgebras of formal vector fields (Q448923)

The authors consider two odd Hamiltonian Lie superalgebras (infinite-dimensional) \(HO\) and \(SHO\) of formal vector fields. There are some natural filtrations on these superalgebras. It is proved in this paper that these natural filtrations of superalgebras \(HO\) and \(SHO\) are invariant under their automorphisms. For some Cartan-type Lie algebras such results are known. The proof is based on the considering of quasi-nilpotent elements. Also the groups of automorphisms of \(HO\) and \(SHO\) are described. It appears that all automorphisms of \(HO\) and \(SHO\) are continuous.