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Cause  Definition  Abbreviation 

Pyroclastic density currents (PDCs)  Pyroclastic flows, surges, and directed blasts  P 
Tephra  Tephra (ash, bombs, lapilli), resultant from both magmatic and phreatic eruptions. Death either by ballistic impact, or, with finergrained ash, by suffocation, collapse of ashcovered roofs etc  T 
Primary Lahars (Mudflows)  Lahars at time of eruption  M 
Indirect  Indirect deaths (disease, starvation, exposure)  I 
Waves (Tsunami)  Waves or tsunami  W 
Secondary Lahars (Mudflows)  Posteruption lahars  m 
Lava Flows  Lava flows  L 
Avalanches  Debris avalanches and landslides  A 
Gas  Gas emission from eruptive craters, as well as fumarolic/ solfataric activity  G 
Seismicity  Seismic, or volcanic earthquake (tectonic earthquake deaths excluded)  S 
Lightning  Lightning strike (electrostatic discharge)  E 
Floods (JГ¶kulhlaups)  Floods and JГ¶kulhlaups  F 

Journal of Lie Theory 26 (2016), No. 4, 10791105 Copyright Heldermann Verlag 2016 Isomorphisms and Rigidity of Arithmetic KacMoody Groups Amir Farahmand Parsa Mathematisches Institut, JustusLiebigUniversitдt, Arndtstrasse 2, 35392 Giessen, Germany [email protected] Max Horn Mathematisches Institut, JustusLiebigUniversitдt, Arndtstrasse 2, 35392 Giessen, Germany [email protected] Ralf Kцhl Mathematisches Institut, JustusLiebigUniversitдt, Arndtstrasse 2, 35392 Giessen, Germany [email protected] We solve the isomorphism problem for subgroups of integral points of twospherical KacMoody groups over the rational numbers. Along the way we establish versions of MostowMargulis strong rigidity and Margulis superrigidity with target in twospherical split KacMoody groups over the rational numbers for arithmetically defined subgroups. Keywords: Arithmetic KacMoody group, twin building, isomorphism problem, MostowMargulis strong rigidity, Margulis superrigidity. MSC: 20G44, 20G25, 51E24 [ Fulltextpdf (444 KB)] for subscribers only. 

Journal of Lie Theory 26 (2016), No. 4, 10791105 Copyright Heldermann Verlag 2016 Isomorphisms and Rigidity of Arithmetic KacMoody Groups Amir Farahmand Parsa Mathematisches Institut, JustusLiebigUniversitдt, Arndtstrasse 2, 35392 Giessen, Germany [email protected] Max Horn Mathematisches Institut, JustusLiebigUniversitдt, Arndtstrasse 2, 35392 Giessen, Germany [email protected] Ralf Kцhl Mathematisches Institut, JustusLiebigUniversitдt, Arndtstrasse 2, 35392 Giessen, Germany [email protected] We solve the isomorphism problem for subgroups of integral points of twospherical KacMoody groups over the rational numbers. Along the way we establish versions of MostowMargulis strong rigidity and Margulis superrigidity with target in twospherical split KacMoody groups over the rational numbers for arithmetically defined subgroups. Keywords: Arithmetic KacMoody group, twin building, isomorphism problem, MostowMargulis strong rigidity, Margulis superrigidity. MSC: 20G44, 20G25, 51E24 [ Fulltextpdf (444 KB)] for subscribers only. 