Extensions of AdS₅ x S⁵ and the Plane-wave Superalgebras and Their Realization in the Tiny Graviton Matrix Theory

In this paper we consider all consistent extensions of the AdS_5 x S^5 superalgebra, psu(2,2|4), to incorporate brane charges by introducing both bosonic and fermionic (non)central extensions. We study the Inonu-Wigner contraction of the extended psu(2,2|4) under the Penrose limit to obtain the most general consistent extension of the plane-wave superalgebra and compare these extensions with the possible BPS (flat or spherical) brane configurations in the plane-wave background. We give an explicit realization of some of these extensions in terms of the Tiny Graviton Matrix Theory (TGMT)[hep-th/0406214] which is the 0+1 dimensional gauge theory conjectured to describe the DLCQ of strings on the AdS_5 x S^5 and/or the plane-wave background.