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The gravitational charge algebra of generic asymptotically locally (A)dSspacetimes is derived in $n$ dimensions. The analysis is performed in theStarobinsky/Fefferman-Graham gauge, without assuming any further boundarycondition than the minimal falloffs for conformal compactification. Inparticular, the boundary structure is allowed to fluctuate and plays the roleof source yielding some symplectic flux at the boundary. Using the holographicrenormalization procedure, the divergences are removed from the symplecticstructure, which leads to finite expressions. The charges associated withboundary diffeomorphisms are generically non-vanishing, non-integrable and notconserved, while those associated with boundary Weyl rescalings arenon-vanishing only in odd dimensions due to the presence of Weyl anomalies inthe dual theory. The charge algebra exhibits a field-dependent $2$-cocycle inodd dimensions. When the general framework is restricted to three-dimensionalasymptotically AdS spacetimes with Dirichlet boundary conditions, the$2$-cocycle reduces to the Brown-Henneaux central extension. The analysis isalso specified to leaky boundary conditions in asymptotically locally (A)dSspacetimes that lead to the $\Lambda$-BMS asymptotic symmetry group. In theflat limit, the latter contracts into the BMS group in $n$ dimensions.

Charge Algebra in Al(A)dS$_n$ Spacetimes