Some remarks on $\mathrm{K}_0$ of noncommutative tori

Abstract

Using Rieffel's construction of projective modules over higher dimensional noncommutative tori, we construct projective modules over some continuous field of C*-algebras whose fibres are noncommutative tori. Using a result of Echterhoff et al., our construction gives generators of $\mathrm {K}_0$ for all noncommutative tori.