# q-Virasoro and q-Heisenberg algebras

The literature has definitions (seemingly plural, though they might be linked) of a $q$-deformed Virasoro algebra. But is there any link of these to a $q$-deformed Heisenberg algebra? (Classically there is an expression for $L_n$ in terms of a normal ordered quadratic in the generators of the Heisenberg algebra.) I would be grateful for a reference to somewhere that discusses this in terms understandable to a non-expert in conformal field theory. However anything to shed light on the current status of the q-Virasoro and q-Heisenberg algebras, or relates them to the undeformed theory, would be of interest.

Apologies for my ignorance on this subject, as I pointed out I am certainly not an expert in CFT. I am currently trying to sort this out as an example of the action of vector fields in noncommutative geometry...

• In particular, there seems to be no reference to $s_{n+m}$ in the commutator of $\{s_n,s_m\}$. – Edwin Beggs Oct 9 '15 at 12:28