Split fins can be caused by physical damage at times such as breeding or heavy feeding times - but it can also indicate Flukes.

It's true. When I see a collection in which the tails are notched, and the pectorals are split, I consider it imperative to get a scope study done on the fish. You'll often find flukes. 

To repair a split pectoral fin can be a quite a difficult job, First of all you should  anesthetise the fish and then using a suitable surgical needle and thread try to sew the fin back together with a fine 3-0 or finer thread, then by weaving the suture through the rays of the fin and eventually closing the gap you must then hope that the threads do not pull through or split the ray next to the ones that you are trying to repair.

The suture should break down in a week under water and the fin, hopefully will be as good as new.

I have tried that wonderful product 'Super Glue' .. but unfortunately as soon as the fish is returned to the water the glue breaks down and we end up at square one ..  so if there is someone out there that has a super glue that will work under water .. please let me know ... 

If the tear is not so bad then the best way is to simply apply a good topical dressing such as Koi Doc or any other good proprietary brand that you can trust. One treatment that I have found to be extremely effective is Silver Nitrate /... this is available from Veterinary Surgeries and perhaps some of the better privately owned Chemists on the high street - this is best applied using the specially prepared Silver Nitrate sticks, that resemble a long match with the head being the Silver Nitrate treatment ... this should be dipped into a something like an egg cup of warm, not hot, water to soften it for a split second ... and then applied to the spit fin along each edge .. Care when using these Silver Nitrate applications, so that you do not get it on your hands or even the work top you may be working on .. as it will badly stain whatever it touches ... even though initially the stain will not show - but 5 minutes later - oh dear !