Early Search for Supersymmetry at ATLAS

The search for physics beyond the Standard Model (BSM) is one of the most important goals for the general purpose detector ATLAS at the Large Hadron Collider at CERN. Supersymmetry search strategies based on generic event signatures of high jet multiplicity and large missing transverse momentum, optionally including leptons in the final state with R-parity conservation are discussed in this document. We review the results for above SUSY search strategies with first data up to 305 $nb^{-1}$ of integrated luminosity collected by ATLAS during 2010 at a centre-of-mass energy of 7 TeV.Comment: 6 pages, to appear in the Proceedings of Kruge 2010 Workshop on Discovery Physics at the LHC, South Africa, 5-10 Dec 2010, available on the CERN document server under the number ATL-PHYS-PROC-2011-01

Existence of Hopf subalgebras of GK-dimension two

Let $H$ be a pointed Hopf algebra over an algebraically closed field of characteristic zero. If $H$ is a domain with finite Gelfand-Kirillov dimension greater than or equal to two, then $H$ contains a Hopf subalgebra of Gelfand-Kirillov dimension two.Comment: Accepted by Journal of Pure and Applied algebra, 10.1016/j.jpaa.2011.04.01