Functional class closed under the induced product

Determine a functional class of non-polynomial generating functions that is closed under the induced on-shell higher-spin product and supports nontrivial interaction equations.

Background

The explicit construction in the paper is restricted to polynomial representatives. However, a gauge connection containing generators of spin greater than two generally involves all spins, so nontrivial interaction equations require power series or another larger functional class.

The paper states that constructing such a class is beyond its scope. Closure under the induced product is necessary for extending the polynomial factor-algebra realization to the interacting on-shell system.

References

Finally, the present analysis is restricted to polynomials, whereas nontrivial interaction equations require a functional class closed under the induced product; this question will be addressed in .

— An explicit product for the on-shell higher-spin algebra in $AdS_d$-space  (2610.26704 - Povarnin, 19 Oct 2026) in Section 4.1, 'On-shell HS algebra'; Conclusion