S 7 andŠ 7

S. Babbage 7,

This documents states the research agenda for the future of cryptology. We show which areas deserve more research bridging the gap between applications and research. For more detailed problems see the STORK document “D6 – Open Problems in Cryptology”.

Essential Dimensions of a 7 and S 7

We show that Y. Prokhorov’s “Simple Finite Subgroups of the Cremona Group of Rank 3” implies that, over any field of characteristic 0, the essential dimensions of the alternating group, A7, and the symmetric group, S7, are 4.

S 7 via Supermembrane Probe

The spacetime superalgebra via the supermembrane probe in the background of AdS4× S is discussed to the lowest order in the spinor coordinate θ. To obtain the correct spacetime superalgebras, all θ order corrections for supervielbein and super 3-form gauge potential have to be included. The central extension of the superalgebra OSp(8|4) of the super isometries for AdS4 × S 7 is found. e-mail ad...

The M - Theory Two - Brane in AdS 4 × S 7 and AdS 7 × S 4

We construct the supermembrane action in an AdS4 ×S 7 and AdS7 ×S 4 background to all orders in anticommuting coordinates. The result is compared to and agrees completely with results obtained earlier for generic supergravity backgrounds through gauge completion at low orders in θ.

Super M - brane actions in adS 4 × S 7 and adS 7 × S 4