Найдены все однородные пространства X = G/H алгебраических групп с одномерным стабилизатором, для которых действие G : T * X коизотропно (т. е. касательное пространство общей G-орбиты коизотропно). Библиография: 10 наименований. Ключевые слова: коммутативные однородные пространства, действия алгебраических групп. § 1. Введение Пусть G-некоторая комплексная алгебраическая группа и H-ее алгебраическая подгруппа. Работа выполнена при финансовой поддержке РФФИ (грант № 09-01-00648a), Федерального агентства по науке и инновациям в рамках госконтракта № 02.740.11.5029. c

Supermassive primordial stars are expected to form in a small fraction of massive protogalaxies in the early universe, and are generally conceived of as the progenitors of the seeds of supermassive black holes (BHs). Supermassive stars with masses of ∼55,000 M , however, have been found to explode and completely disrupt in a supernova (SN) with an energy of up to ∼10 55 erg instead of collapsing to a BH. Such events, ∼10,000 times more energetic than typical SNe today, would be among the biggest explosions in the history of the universe. Here we present a simulation of such a SN in two stages. Using the RAGE radiation hydrodynamics code, we first evolve the explosion from an early stage through the breakout of the shock from the surface of the star until the blast wave has propagated out to several parsecs from the explosion site, which lies deep within an atomic cooling dark matter (DM) halo at z 15. Then, using the GADGET cosmological hydrodynamics code, we evolve the explosion out to several kiloparsecs from the explosion site, far into the low-density intergalactic medium. The host DM halo, with a total mass of 4 × 10 7 M , much more massive than typical primordial star-forming halos, is completely evacuated of high-density gas after 10 Myr, although dense metal-enriched gas recollapses into the halo, where it will likely form second-generation stars with metallicities of 0.05 Z after 70 Myr. The chemical signature of supermassive star explosions may be found in such long-lived second-generation stars today.