The physics of ``particles of spin $\leq 2$'' leads to representations of a
Lie algebra $\Xi$ of gauge parameters on a vector space $\Phi$ of fields.
Attempts to develop an analogous theory for spin $>2$ have failed; in fact,
there are claims that such a theory is impossible (though we have been unable
to determine the hypotheses for such a `no-go' theorem). This led BBvD
[burgers:diss,BBvd:three,BBvD:probs] to generalize to `field dependent
parameters' in a setting where some analysis in terms of smooth functions is
possible. Having recognized the resulting structure as that of an sh-lie
algebra ($L_\infty$-algebra), we have now reproduced their structure entirely
algebraically, hopefully shedding some light on what is going on.