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An algebraic background for construction of hierarchies of PDE in dimension (2|1) Roger, Claude


In d=2 with variables (x,t), the superalgebraic trick of adding a supplementary odd variable allows the construction of a "square root of time", an operator D satisfying D^2=∂/∂t in superspace of dimension (2|1). We used it to obtain a Miura transform in dimension (2|1) for non stationary Schrödinger type operators. We shall discuss here the construction of an algebra of pseudodifferential symbols in dimension (2|1); that algebra generalizes the one for d=1, used in construction of hierarchies from isospectral deformations of stationary Schrödinger type operators.

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