Walters, Sam Periodic integral transforms and associated noncommutative orbifold projections. (English) Zbl 1349.46083 C. R. Math. Acad. Sci., Soc. R. Can. 37, No. 3, 114-120 (2015). Summary: We report on recent results on the existence of cubic and hexic integral transforms on self-dual locally compact groups (orders 3 and 6 analogues of the classical Fourier transform) and their application in constructing a canonical continuous section of smooth projections \({\mathcal E}(t)\) of the continuous field of rotation \(C^*\)-algebras \(\{A_t\}_{0<t<1}\) that is invariant under the noncormutative hexic transform automorphism. This leads to invariant matrix (point) projections of the irrational noncommutative tori \(A_\theta\). We also present a quick method for computing the (quantized) topological invariants of such projections using techniques from classical theta function theory. MSC: 46L85 Noncommutative topology 46L05 General theory of \(C^*\)-algebras 57R18 Topology and geometry of orbifolds Keywords:\(C^\ast\)-algebra; orbifold; symmetries; automorphisms; noncommutative tori; rotation algebra; Fourier transform; inductive limits; unbounded traces; topological invariants PDFBibTeX XMLCite \textit{S. Walters}, C. R. Math. Acad. Sci., Soc. R. Can. 37, No. 3, 114--120 (2015; Zbl 1349.46083)