Year: 2026
Type: preprint
Abstract: We introduce source-anchored algebraic amenability for Hausdorff ample groupoids, a Følner condition formulated in the Steinberg algebra and localized at compact open subsets of the unit space. The unanchored bisectional condition is exactly algebraic amenability of the Steinberg algebra, whereas the anchored version recovers ordinary amenability for one-unit groupoids and detects behavior invisible to the unanchored theory. We establish permanence under isomorphisms, open invariant reductions, disjoint unions, finite products, directed unions and AF approximations, while arbitrary subgroupoids need not inherit the property. For countable transitive discrete groupoids, infinite unit spaces are amenable through range escape, whereas finite unit spaces are amenable precisely when their isotropy groups are. This yields a characterization of hereditary algebraic amenability in terms of isotropy.
Source: arXiv (Cornell University)
Authors: Herrera, Karol, Rubiano, Andrés
Institution: Escuela Colombiana de Carreras Industriales
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7216077251