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We construct new extensions of current and diffeomorphism algebras in N>3dimensions, which are related to the Mickelsson-Faddeev algebra. The result iscompatible with Dzhumadil'daev's classification of diffeomorphism cocycles. Wealso construct an extension of the current algebra in N>=5 dimensions whichdepends on the fourth Casimir operator.

Covariant Mickelsson-Faddeev extensions of gauge and diffeomorphism algebras