Infinite-Dimensional Modular Odd Hamiltonian Superalgebras

Abstract

The natural filtrations of the infinite-dimensional modular odd hamiltonian superalgebras are proved to be invariant under automorphism. The proof involves the investigation of the ad-nilpotent elements of the even part, and the determination of the subalgebras generated by certain ad-nilpotent elements. We are thereby able to obtain an intrinsic characterization of odd hamiltonian superalgebras and establish a property of automorphisms of these Lie superalgebras.

Key Words:

• Odd Hamiltonian superalgebras
• ad-nilpotent elements
• p-adic matrices

Mathematics Subject Classification:

• Primary 17B50
• Secondary 17B05, 17B65

Acknowledgment

The authors are grateful to the referee for his useful and valuable suggestions.

Notes

^#Communicated by K. Misra.