Fourier Analysis Meets Quantum Groupoids: Towards a Noncommutative Harmonic Framework for Local Symmetries

Taipe F. · Trends in Mathematics (2026) · DOI: 10.1007/978-3-032-14211-5_21

Resumen

Operator algebraic quantum groups and operator algebraic quantum groupoids offer powerful frameworks for generalising classical notions of groups and groupoids within the realms of analysis, geometry and representation theory. This work provides an expository survey of the extension of Fourier theory from the classic setting of abelian groups to these quantum contexts, with particular emphasis on the reformulation of classical constructions to accommodate noncommutative structures. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2026.

Instituciones: Universidad Nacional de Ingeniería