too little charging current -> Lima defective?

Hello everybody, it’s about the V50 1.6D – BJ 2008 – 130,000km the following problem: In recent times the message “Warning, checking the electrical system” accumulates shortly after the start (sometimes also on the AB when many breakers are on). The message usually disappears after a two minutes. In the connection also messages about the failure div. sensors appear. I then switched on suspicion the battery. After some time, especially now that it got cold again, the M eldungen again until the car was standing one night after a 2h motorway ride (at approx. -2°C) and then did not have enough juice to jump around. At the measure arrives at the battery after the start ~11,9 V and commutes after a few minutes to ~13,4V (without builder heating/radio/light). Does therefore seem def. to be the Lima? Are there other sources of error? Contacts at Lima seem to be fine. Had thought of changing the carbon brushes first when I replaced the Lima If I do, can I expand it myself without much effort? Then I would completely exchange it. Thank you for your answers!