While permissions is not an extensibility point the Telligent Evolution platform does offer APIs for viewing and managing permissions.
In-process API permissions methods: http://telligent.com/community/developers/w/developer7/28959.permissions-in-process-api-service.aspx
REST API permissions endpoints: http://telligent.com/community/developers/w/developer7/29504.permission-rest-endpoints.aspx
Because permissions are assigned to roles, also review the In-process and REST APIs for viewing and managing roles including adding a user to a role, removing a user from a role, etc.
Examples and demonstrations
Alex Crome created a permission viewer application that is both useful as a diagnostics tool and as a good reference example for working with the Telligent Evolution REST roles and permissions endpoints.
Find Alex's Telligent Evolution Permission Viewer on GitHub.
The permission viewer application is a diagnostic tool for viewing permissions in the Telligent Evolution platform. It allows you to view permissions in a tabular form which can make diagnosing permission based issues easier.
It uses the Telligent Evolution platform REST API to pull data out of a Telligent Evolution platform community.