I have positve criticism of your abstract in presentation. Consider me just a reader, trying to understand and see if I am interested in reading further.
I'm a physicist not a philosopher, so I need some added reminder or hint about what didactic means.
Give an example with motivational argument to show similarity. Get rid of the (--) and use standard English.
Again, show by comparison of the usage of Lie algebra's in classical and quantum physics to motivate comparison.
This one is a giant step. You need more motivation for making this claim within your abstract. Give a few more details and defer it to the main body of the text using a phrase such as "as will be demonstarted". This should be a good half of your abstract.
I hope this helps on the frontier of written communication.