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Hello How do I add a lightweight access point AIR-LAP1131AG-A-K9 to the network and then have it managed by the LAP4402 controller
You can "prime" the access point by manually/directly configuring items like the AP's IP address and the IP address of the controller, or you can use DNS/DHCP to allow the AP to automagically discover the controller.
Here are a few links worth reading:
(if you are not running 5.2 code on your controller, just grab the same section from the relevant 4.2/5.1 config guide)