Abstract
We compute the Wodzicki residue of the inverse of a conformally rescaled Laplace operator over a 4-dimensional noncommutative torus. We show that the straightforward generalization of the Laplace-Beltrami operator to the noncommutative case is not the minimal operator.
Highlights
Noncommutative geometry as proposed in [2] aims to use geometric methods to study noncommutative algebras in a similar way that differential geometry is used to study spaces
The construction of basic data in noncommutative geometry is equivalent in the classical case to the standard data of Riemannian geometry [1] in the genuine noncommutative examples this aspect has not been sufficiently explored until recently
In a series of papers first [3,4] and [7,8,9,10,11,12] a conformally rescaled metric has been proposed and studied for the noncommutative two and four-tori. This led to the expressions of Gauss-Bonnet theorem and formulae for the noncommutative counterpart of scalar curvature
Summary
Noncommutative geometry as proposed in [2] aims to use geometric methods to study noncommutative algebras in a similar way that differential geometry is used to study spaces. In a series of papers first [3,4] and [7,8,9,10,11,12] a conformally rescaled metric has been proposed and studied for the noncommutative two and four-tori This led to the expressions of Gauss-Bonnet theorem and formulae for the noncommutative counterpart of scalar curvature. In the classical case the computation of second heat kernel coefficient is closely related to the computations of the Wodzicki residue of a certain power of the Dirac operator As it has been shown [12] and more generally in [15] Wodzicki residue exists in the case of the pseudodifferential calculus over noncommutative tori.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
