Central extensions preserve bounded locality for finite-type Lie conformal algebras

Let $\goth L$ be a finite-type Lie conformal algebra generated by a finite set $\cal G$, and suppose its locality function satisfies

$$S_{\goth L,\cal G}(l)<K.$$

Let $M$ be a $\mathds k[D]$-module generated by a set $\cal M$, on which $\goth L$ acts trivially, and let $\widehat{\goth L}$ be a central extension of $\goth L$. The locality function of the extension with respect to $\cal G\cup\cal M$ is said to be uniformly bounded when it is bounded independently of the word length.

Central-extension bounded-locality conjecture. The locality function $S_{\widehat{\goth L},\,\cal G\cup\cal M}$ is also uniformly bounded.

The paper notes that central extensions of loop algebras provide examples with bounded locality and suggests this conjecture as a general mechanism for producing further examples. Its validity is left open.