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\begin{abstract} By following the paradigm of the global quantisation,instead of the analysis under changes of coordinates, in this work we establisha global analysis for the explicit computation of the Dixmier trace and theWodzicki residue of (elliptic and subelliptic) pseudo-differential operators oncompact Lie groups. The regularised determinant for the Dixmier trace is alsocomputed. We obtain these formulae in terms of the global symbol of thecorresponding operators. In particular, our approach links the Dixmier traceand Wodzicki residue to the representation theory of the group. Although westart by analysing the case of compact Lie groups, we also compute the Dixmiertrace and its regularised determinant on arbitrary closed manifolds $M$, forthe class of invariant pseudo-differential operators in terms of theirmatrix-valued symbols. This analysis includes e.g. the family of positive andelliptic pseudo-differential operators on $M$.

Dixmier traces, Wodzicki residues, and determinants on compact Lie groups: the paradigm of the global quantisation