Relation between de Sitter and Poincare Groups

[Raifeartagh]

Hi,

I have a question about groups: What is the de Sitter group?? and how does it relate to poncaire's group?

Thanks!

 

[robphy]

This may be useful
https://www.physicsforums.com/showthread.php?t=126285
(I haven't read through it myself.)

 

[strangerep]

What is the de Sitter group?? and how does it relate to poncaire's group?

Your question needs to be a bit more specific. Since you asked in a relativity forum, I guess you're interested in possible physical applications, not just the math. You could try looking up Wikipedia for "de Sitter space" and "de Sitter relativity", in which the de Sitter group is the invariance group, just as the Poincare group is the invariance group applicable in Minkowski spacetime.

De Sitter space is also one of the few spaces of constant curvature, and one generally introduces an associated universal length constant which some researchers (speculatively) try to relate to the cosmological constant $\Lambda$. In a limit as we take this length constant very large, de Sitter contracts to Poincare. (Here I use the word "contracts" in the sense of group contraction, i.e., similarly to how the Poincare group contracts to the Galilei group in the limit as $c \to \infty$.)