Non-virtually abelian discontinuous group actions vs. proper SL(2,R)-actions on homogeneous spaces

2022/06/02 by Bochenski, Maciej, de Graaf, Willem A., Jastrzebski, Piotr +1
#17B05 #17B10 #53C30 #57S25 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2206.01069

Abstract

We develop algorithms and computer programs which verify criteria of properness of discrete group actions on semisimple homogeneous spaces. We apply these algorithms to find new examples of non-virtually abelian discontinuous group actions on homogeneous spaces which do not admit proper SL(2,R)-actions.

Related

• Homogeneous space with non virtually abelian discontinuous groups but without any proper SL(2,R)-action
• Proper actions on strongly regular homogeneous spaces
• A note on properly discontinuous actions
• Sharpness of proper and cocompact actions on reductive homogeneous spaces
• Exotic proper actions on homogeneous spaces via convex cocompact representations