Month: July 2017

In my search for less abstract or trivial examples of a universal enveloping algebra, I have come upon this one. Let be a vector space and a free associative algebra on . The mapping is a vector space morphism . can also be viewed as a Lie algebra. is a part of ; let be…

This keeps cropping up, and every time it takes me some effort to rediscover the proof. It happened first with free groups, then with free vector spaces and again with free Lie algebras. I’ll formulate the issue with groups, but it is easy to carry it over to other cases. A free group on set…