A Two Dimensional Adler-Manin Trace and Bi-singular Operators
  Motivated by the theory of bi-singular pseudodifferential operators, we introduce a two dimensional version of the Adler-Manin trace. Our construction is rather general in the sense that it involves a twist afforded by an algebra automorphism. That is, starting from an algebra equipped with an automorphism, two twisted derivations, and a twisted invariant trace, we construct an algebra of formal twisted pseudodifferential symbols and define a noncommutative residue. Also, we provide related examples. 
Farzad Fathizadeh, Masoud Khalkhali, Fabio Nicola, Luigi Rodino
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