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Journal of Lie Theory 26 (2016), No. 4, 1079--1105
Copyright Heldermann Verlag 2016



Isomorphisms and Rigidity of Arithmetic Kac-Moody Groups

Amir Farahmand Parsa
Mathematisches Institut, Justus-Liebig-Universitдt, Arndtstrasse 2, 35392 Giessen, Germany
[email protected]

Max Horn
Mathematisches Institut, Justus-Liebig-Universitдt, Arndtstrasse 2, 35392 Giessen, Germany
[email protected]

Ralf Kцhl
Mathematisches Institut, Justus-Liebig-Universitдt, Arndtstrasse 2, 35392 Giessen, Germany
[email protected]



We solve the isomorphism problem for subgroups of integral points of two-spherical Kac-Moody groups over the rational numbers. Along the way we establish versions of Mostow-Margulis strong rigidity and Margulis superrigidity with target in two-spherical split Kac-Moody groups over the rational numbers for arithmetically defined subgroups.

Keywords: Arithmetic Kac-Moody group, twin building, isomorphism problem, Mostow-Margulis strong rigidity, Margulis superrigidity.

MSC: 20G44, 20G25, 51E24

[ Fulltext-pdf  (444  KB)] for subscribers only.


В Modality (device)В ParameterВ AdvantagesВ DisadvantagesВ 
Regional stiffnessВ DopplerВ cfPWVaВ 
  • Inexpensive, portable

  • Can assess other cardiac and arterial features, e.g. LV hypertrophy, strain

  • Does not require a specific device

  • Faster than applanation tonometry

  • Identification of anatomical landmarks aids repeatability of measurement position

  • Can detect occlusive/atherosclerotic lesions that may affect PWV

В 
  • Operator-dependent skill

  • Sites of measurement limited by acoustic window

  • Lacks versatility for anatomical variations

  • Method of distance measurement overestimates distance

  • Calculation of cfPWV includes iliac and femoral arteries and excludes ascending aorta

In addition:
  • Transit time is determined through visual assessment using digital calipers, limited by temporal resolution

В 
Mechano- transducer (Complior)В cfPWVВ 
  • Similar to Doppler

In addition:
  • Automated device

  • Simultaneous measurements

В 
  • Similar to Doppler

In addition:
  • Variations in transit time algorithms used

  • Underestimates PWV compared with applanation tonometry

  • Cannot provide local wall assessment, where aortic condition may vary

В 
Applanation tonometry (SpyghmoCor)В cfPWVВ 
  • Inexpensive, portable

В 
  • Similar to Doppler

In addition:
  • Two consecutive recordings needed, heart rate variability may cause confounding

  • Local wall assessment not possible

В 
Local stiffnessВ CMRВ aPWV and ADВ 
  • Local and regional assessment of aorta possible

  • Relatively operator independent

  • Full visualization of the entire vessel

  • Imaging planes can be precisely placed with good repeatability

  • Greater spatial and temporal resolution (especially 3Tesla CMR) to study the temporal shift over smaller distances

  • Measurement not affected by anatomical variations, peripheral vascular disease or problems with using probes to detect waveforms

  • Other aspects of cardiac and arterial function can be assessed, e.g. strain and deformation

В 
  • Focal measurement may be prone to sampling error

  • Image analysis can be time-consuming and user dependent

  • Expensive

  • Longer examination time than other methods

  • Not possible with patients with metal implants, or with claustrophobia

  • PP is usually determined non-invasively and peripherally as it is more feasible than invasive measurement

В 
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Xvideos, --RICHARD STRAFFORD'S LETTER FROM THE BERMUDAS.  xvideos xx fucp was shortly afterwards that I allowed my hobby for-- playing at forts to run away with me.

Xvideos, --RICHARD STRAFFORD'S LETTER FROM THE BERMUDAS. xvideos xx fucp was shortly afterwards that I allowed my hobby for-- playing at forts to run away with me.


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