Standard and Non-standard Extensions of Lie algebras

We study the problem of quadruple extensions of simple Lie algebras. We find that, adding a new simple root $\alpha_{+4}$, it is not possible to have an extended Kac-Moody algebra described by a Dynkin-Kac diagram with simple links and no loops between the dots, while it is possible if $\alpha_{+4}$ is a Borcherds imaginary simple root. We also comment on the root lattices of these new algebras. The folding procedure is applied to the simply-laced triple extended Lie algebras, obtaining all the non-simply laced ones. Non- standard extension procedures for a class of Lie algebras are proposed. It is shown that the 2-extensions of $E_{8}$, with a dot simply linked to the Dynkin-Kac diagram of $E_{9}$, are rank 10 subalgebras of $E_{10}$. Finally the simple root systems of a set of rank 11 subalgebras of $E_{11}$, containing as sub-algebra $E_{10}$, are explicitly written.Comment: Revised version. Inaccurate statements corrected. Expanded version with added reference

Galaxy Orientations in the Coma Cluster

We have examined the orientations of early-type galaxies in the Coma cluster to see whether the well-established tendency for brightest cluster galaxies to share the same major axis orientation as their host cluster also extends to the rest of the galaxy population. We find no evidence of any preferential orientations of galaxies within Coma or its surroundings. The implications of this result for theories of the formation of clusters and galaxies (particularly the first-ranked members) are discussed.Comment: Accepted for publication in the Astrophysical Journal Letters. 4 pages, 4 figure

Resistively-Detected NMR in a Two-Dimensional Electron System near ν=1\nu = 1: Clues to the Origin of the Dispersive Lineshape

Resistively-detected NMR measurements on 2D electron systems near the $\nu = 1$ quantum Hall state are reported. In contrast to recent results of Gervais \emph{et al.} [Phys. Rev. Lett. $\bf 94$, 196803 (2005)], a dispersive lineshape is found at all RF powers studied and Korringa-like nuclear spin-lattice relaxation is observed. The shape of the unexplained dispersive lineshape is found to invert when the temperature derivative of the longitudinal resistance changes sign. This suggests that both Zeeman and thermal effects are important to resistively-detected NMR in this regime.Comment: 5 pages, 4 figures. Version accepted for publication in Phys. Rev.B, Rapid Communication

Spin Transition in the Half-Filled Landau Level

The transition from partial to complete spin polarization of two-dimensional electrons at half filling of the lowest Landau level has been studied using resistively-detected nuclear magnetic resonance (RDNMR). The nuclear spin-lattice relaxation time is observed to be density independent in the partially polarized phase but to increase sharply at the transition to full polarization. At low temperatures the RDNMR signal exhibits a strong maximum near the critical density.Comment: 4 pages, 3 postscript figures. As published in Phys. Rev. Lett. 98, 086801 (2007

Nonconventional odd denominator fractional quantum Hall states in the second Landau level

We report the observation of a new fractional quantum Hall state in the second Landau level of a two-dimensional electron gas at the Landau level filling factor $\nu=2+6/13$. We find that the model of noninteracting composite fermions can explain the magnitude of gaps of the prominent 2+1/3 and 2+2/3 states. The same model fails, however, to account for the gaps of the 2+2/5 and the newly observed 2+6/13 states suggesting that these two states are of exotic origin.omposite fermion model. However, the weaker 2+2/5 and 2+6/13 states deviate significantly suggesting that these states are of exotic origin

Quantum Hall Exciton Condensation at Full Spin Polarization

Using Coulomb drag as a probe, we explore the excitonic phase transition in quantum Hall bilayers at nu=1 as a function of Zeeman energy, E_Z. The critical layer separation d/l for exciton condensation initially increases rapidly with E_Z, but then reaches a maximum and begins a gentle decline. At high E_Z, where both the excitonic phase at small d/l and the compressible phase at large d/l are fully spin polarized, we find that the width of the transition, as a function of d/l, is much larger than at small E_Z and persists in the limit of zero temperature. We discuss these results in the context of two models in which the system contains a mixture of the two fluids.Comment: 4 pages, 3 eps figure