The Spacetime Superalgebras from M-branes in M-brane Backgrounds

We derive the spacetime superalgebras explicitly from ``test'' M-brane actions in M-brane backgrounds to the lowest order in $\theta$ via canonical formalism, and discuss various BPS saturated configurations on the basis of their central charges which depend on the harmonic functions determined by the backgrounds. All the 1/4 supersymmetric intersections of two M-branes obtained previously are deduced from the requirement of the test branes to be so ``gauge fixed'' in the brane backgrounds as to preserve 1/4 supersymmetry. Furthermore, some of 1/2-supersymmetric bound states of two M-branes are deduced from the behavior of the harmonic functions in the limits of vanishing distances of the two branes. The possibilities of some triple intersections preserving 1/4 supersymmetry are also discussed.