Are you sure that the nail is actually split? Sometimes when the outer layers of the nail are being shed, it kinda looks like the nail is split. Unless there is blood or your kitty is in pain, I would leave it alone. If it looks serious and your kitty is in pain, maybe you should see a vet.
By "embedded" are you talking about the nail growing in the pad? If so, you need a vet to look at it. All nails should be kept trimmed so this does not happen.