2021/05/31 by Duván Cardona, Julio Delgado, Cardona, Duván +3
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #Homotopy and Cohomology in Algebraic Topology #math.DG #math.FA
paper · pdf · doi:10.48550/arxiv.2105.14949
31 pages
arxiv created 2021/05/31 · openalex publication_date 2021/05/31 · arxiv updated 2021/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
\beginabstract By following the paradigm of the global quantisation, instead of the analysis under changes of coordinates, in this work we establish a global analysis for the explicit computation of the Dixmier trace and the Wodzicki residue of (elliptic and subelliptic) pseudo-differential operators on compact Lie groups. The regularised determinant for the Dixmier trace is also computed. We obtain these formulae in terms of the global symbol of the corresponding operators. In particular, our approach links the Dixmier trace and Wodzicki residue to the representation theory of the group. Although we start by analysing the case of compact Lie groups, we also compute the Dixmier trace and its regularised determinant on arbitrary closed manifolds M, for the class of invariant pseudo-differential operators in terms of their matrix-valued symbols. This analysis includes e.g. the family of positive and elliptic pseudo-differential operators on M.