Local invariants of conformally deformed non-commutative tori II
Multiple operator integrals
T. D.H. van Nuland (TU Delft - Analysis)
Fedor Sukochev (University of New South Wales)
Dmitriy Zanin (University of New South Wales)
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Abstract
We explicitly compute the local invariants (heat kernel coefficients) of a conformally deformed non-commutative d-torus using multiple operator integrals. We derive a recursive formula that easily produces an explicit expression for the local invariants of any order k and in any dimension d. Our recursive formula can conveniently produce all formulas related to the modular operator, which before were obtained in incremental steps for d∈{2,3,4} and k∈{0,2,4}. We exemplify this by writing down some known (k=2, d=2) and some novel (k=2, d≥3) formulas in the modular operator.
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