in Blumenhagen Book on conformal field theory, It is mentioned that the algebra of infinitesimal conformal transformation is different from the conformal algebra and on page 11, conformal algebra is defined by a redefinition of generators of infinitesimal conformal transformation. I have three question about this :

How this is possible that by a redefinition of generators, one could obtain a sub-algebra of an algebra? in this case one obtain conformal algebra as a sub-algebra of algebra of generators of infinitesimal conformal transformations?

Does this is related to «special conformal transformation» which is not globally defined?

How are these related to topological properties of conformal group?

Any comment or reference would greatly be appreciated!

This post imported from StackExchange Physics at 2015-05-27 20:59 (UTC), posted by SE-user QGravity