The Seven-sphere and its Kac-Moody Algebra

We investigate the seven-sphere as a group-like manifold and its extension to a Kac-Moody-like algebra. Covariance properties and tensorial composition of spinors under $S^7$ are defined. The relation to Malcev algebras is established. The consequences for octonionic projective spaces are examined. Current algebras are formulated and their anomalies are derived, and shown to be unique (even regarding numerical coefficients) up to redefinitions of the currents. Nilpotency of the BRST operator is consistent with one particular expression in the class of (field-dependent) anomalies. A Sugawara construction is given.Comment: 22 pages. Macropackages used: phyzzx, epsf. Three epsf figure files appende

Changes in the volume and salinity of Lake Khubsugul (Mongolia) in response to global climate changes in the upper Pleistocene and the Holocene

Two gravity cores (1.1 and 2.2 m long) of deep-water bottom sediments from Lake Khubsugul (Mongolia) were studied. The Holocene, biogenic silica and organic matter-rich part of the first core was subjected to AMS radiocarbon dating which placed the date of dramatic increase of pelagic diatoms (40 cm below sediment surface) at a calendar age of 11.5 cal ky BP. ICP-MS analysis of weak nitric acid extracts revealed that the upper Pleistocene, compared to the Holocene samples, were enriched in Ca, Cinorg, Sr, Mg and depleted of U, W, Sb, V and some other elements. Transition to the Holocene resulted in an increase of total diatoms from 0 to 108 g-1, of BiSi from 1% to 20%, of organic matter from 6%. The Bølling–Allerød–Younger Dryas–Holocene abrupt climate oscillations manifested themselves in oscillations of geochemical proxies. A remarkable oscillation also occurred at 22 cm (ca. 5.5 ky BP). The Pleistocene section of the second, longer core was enriched in carbonate CO2 (up to 10%) and water-extractable SO42- (up to 300 times greater than that in Holocene pore waters). All this evidence is in an accord with the earlier finding of drowned paleo-deltas at ca. 170 m below the modern lake surface of the lake [Dokl. Akad. Nauk 382 (2002) 261] and suggests that, due to low (ca. 110 mm) regional precipitation at the end of the Pleistocene, Lake Khubsugul was only 100 m deep, and that its volume was ca. 10 times less than today