The Aleax, A, is a humanoid angelic being. It can occasionally appear as a lawful minion, or can be found generated randomly outside of Gehennom. It is also the only humanoid angelic monster that is a valid polymorph form.
Aleaxes are generated with blessed erodeproof long swords and non-cursed erodeproof large shields. There is a 1/20 chance that the sword will be converted into either Demonbane or Sunsword (if the chosen artifact does not exist yet), and a 1/4 chance the shield will instead be a shield of reflection.
In Dungeons & Dragons, an Aleax is an avatar of a deity, sent to punish a specific mortal. The Aleax takes on the target's exact appearance and carries identical equipment. For this reason, NetHack's Aleax imitates you when you #chat to it.
In UnNetHack it behaves like the D&D Aleax (which takes on the target's exact appearance and carries identical equipment). It is wearing an erodeproof +0 copy of all of the player's equipment and weapons. Artifacts will be converted to the base item.
An Aleax, according to the AD&D Fiend Folio, is a creature that
looks exactly like the character, and is sent by the character's
god to punish alignment violations. Obviously - and luckily - in
Nethack this is not the case.