Huge Lie superalgebra of pseudo superdifferential operators and super KP-hierarchies

摘要

Lie superalgebraic methods are used to establish a connection between the huge Lie superalgebra Xi of super (pseudo) differential operators and various super KP-hierarchies. We show in particular that Xi splits into 5 = 2 x 2 + 1 graded algebras expected to correspond to five classes of super KP-hierarchies, generalizing the well-known Manin-Radul and Figueroa O'Farrill-Ramos supersymmetric KP-hierarchies. (author). 10 refs. (Atomindex citation 26:077991)