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A two dimensional Adler-Manin trace and bi-singular operators. (English) Zbl 1279.58013

Summary: Motivated by the theory of bisingular 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.

MSC:

58J42 Noncommutative global analysis, noncommutative residues
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