Equivalence of Two Approaches to Yang-Mills on Non-commutative Torus

There are two notions of Yang-Mills action functional in noncommutative geometry. We show that for noncommutative n-torus both these notions agree. We also prove a structure theorem on the Hermitian structure of a finitely generated projective modules over spectrally invariant subalgebras of $C^*$-algebras.

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