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arXiv · 2602.22665

Structural Chirality from Inverse Semigroups to Twisted Groupoid $C^*$-Algebras

Takao Inoué
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Abstract

We develop a structural theory of chirality for inverse semigroups and show how it propagates canonically to \'{e}tale groupoids and twisted groupoid $C^*$-algebras. Starting from inverse semigroup data equipped with admissible twist information, we construct a canonical twisted universal groupoid in the sense of Paterson and introduce a mirror correspondence encoding intrinsic asymmetry. Our main result identifies a structural obstruction to mirror self-duality at the level of twisted universal groupoids and shows that this obstruction descends to an obstruction for the associated reduced twisted groupoid $C^*$-algebra to be isomorphic to its opposite. The framework is representation-independent, yet compatible with concrete germ groupoid models, and provides a unified bridge between partial symmetries, groupoid structures, and analytic invariants in noncommutative operator algebras.

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BibTeXRIS

Takao Inoué. 2026-02-26. Structural Chirality from Inverse Semigroups to Twisted Groupoid $C^*$-Algebras. https://arxiv.org/abs/2602.22665

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