Star-product functions in higher-spin theory and locality

Abstract

Abstract: Properties of the functional classes of star-product elements associated with higher-pin gauge fields and gauge parameters are elaborated. Cohomological interpretation of the nonlinear higher-spin equations is given. An algebra ℋ$$ \mathrm{\mathscr{H}} $$, where solutions of the nonlinear higher-spin equations are valued, is found. A conjecture on the classes of star-product functions underlying (non)local maps and gauge transformations in the nonlinear higher-spin theory is proposed.