Abstract
Vasilievʼs higher-spin (HS) theories in various dimensions are uniformly represented as a simple system of equations. These equations and their gauge invariances are based on two superalgebras and have a transparent algebraic meaning. For a given HS theory these algebras can be inferred from the vacuum HS symmetries. The proposed system of equations admits a concise AKSZ formulation. We also discuss novel HS systems including partially-massless and massive fields in AdS, as well as conformal and massless off-shell fields.
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