Structural Chirality from Inverse Semigroups to Twisted Groupoid $C^*$-Algebras
Abstrak
We develop a structural theory of chirality for inverse semigroups and show how it propagates canonically to étale 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.
Penulis (1)
Takao Inoué
Akses Cepat
- Tahun Terbit
- 2026
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓