  Recently it was proposed that the Bagger-Lambert-Gustavsson theory with
Nambu-Poisson structure describes an M5-brane in a three-form flux background.
In this paper we investigate the superalgebra associated with this theory. We
derive the central charges corresponding to M5-brane solitons in 3-form
backgrounds. We also show that double dimensional reduction of the superalgebra
gives rise to the Poisson bracket terms of a non-commutative D4-brane
superalgebra. We provide interpretations of the D4-brane charges in terms of
spacetime intersections.
