Quantum symmetry groups of Hilbert modules equipped with orthogonal filtrations

TL;DR

This paper introduces the quantum symmetry group for Hilbert modules with orthogonal filtrations, unifying previous concepts in quantum symmetry and isometry groups within a broader mathematical framework.

Contribution

It defines and proves the existence of the quantum symmetry group for Hilbert modules with orthogonal filtrations, extending prior constructions to a more general setting.

Findings

Unified quantum symmetry group construction for Hilbert modules

Generalizes Banica-Skalski and Goswami's frameworks

Establishes existence of the quantum symmetry group

Abstract

We define and show the existence of the quantum symmetry group of a Hilbert module equipped with an orthogonal filtration. Our construction unifies the constructions of Banica-Skalski's quantum symmetry group of a C*-algebra equipped with an orthogonal filtration and Goswami's quantum isometry group of an admissible spectral triple.