Management: you can aquire if you build academies and set taxes to anything above ''high''.
Influence: being a faction leader, or heir helps. A position in the senate also raises your influence. And usually if you conquer a lot of land, you're character 'll likely raise his influence level. Diplomats can raise influence by being a productive diplomat, they can also lose influence if they don't make any good deals.
Loyalty....that's a hard one....I'd say that refusing bribes 'll make a character increase in loyalty, other than that I don 't really know. Sometimes giving generals to large of an army reduces Loyalty, they might get some fancy ideas you know....
I find that once you're beginning to dominate the world, management, influence and command ratings always move down on my priority list. I usually groom one general and try to get him to raise his stats, just for the fun of it.
In the beginning, when cash, armies and land are in a somewhat more worrying state, I do tend to keep more of an eye on my generals. As said, as time progresses, I tend to concentrate on a few ''favorite'' generals.

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