Member of the Poincare or Lorentz Group

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SUMMARY

The discussion centers on the comparison between the Poincaré Group and the Lorentz Group, highlighting that the Poincaré Group is a semidirect product of the Lorentz Group and translations. This structure establishes the Poincaré Group as more powerful than the Lorentz Group, which is a subgroup of the former. Participants express preferences for team names based on these groups, with humorous suggestions like "Diffeomorphists" and "Homeomorphists" to illustrate the flexibility of mathematical group memberships.

PREREQUISITES
  • Understanding of group theory in mathematics
  • Familiarity with the concepts of semidirect products
  • Knowledge of the Lorentz transformations
  • Basic comprehension of mathematical terminology related to topology
NEXT STEPS
  • Research the properties of the Poincaré Group in theoretical physics
  • Study the implications of Lorentz transformations in special relativity
  • Explore the concept of semidirect products in group theory
  • Learn about diffeomorphism and homeomorphism in topology
USEFUL FOR

This discussion is beneficial for mathematicians, physicists, and students interested in group theory, particularly those exploring the foundations of relativity and topology.

Rainbows_
What is more cool... to be a member of the Poincare Group or Lorentz Group?

What name would you choose for a school science team and why?
 
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Chose Poincaré: Two to the price of one!
 
fresh_42 said:
Chose Poincaré: Two to the price of one!

Why is Poincare Group twice or more powerful than Lorentz Group?
 
The Poincaré group is the semidirect product of the Lorentz group and the translations.
 
fresh_42 said:
The Poincaré group is the semidirect product of the Lorentz group and the translations.

If the Poincare is product of Lorentz.. then is it not Lorentz is more powerful?
 
Rainbows_ said:
If the Poincare is product of Lorentz.. then is it not Lorentz is more powerful?
The Lorentz group is a subgroup of the Poincaré group.
 
fresh_42 said:
The Lorentz group is a subgroup of the Poincaré group.

Ok. I'll be a member of the Poincare Group then. Thanks.
 
Heh, why stop there? If you're a member of the "Diffeomorphism Group", you can be (almost) anything you like. :wink:
 
strangerep said:
the "Diffeomorphism Group"
Or maybe the "Diffeomorphists" or "Diffeomorphers". :cool:
 
  • #10
jtbell said:
Or maybe the "Diffeomorphists" or "Diffeomorphers". :cool:
I prefer the Homeomorphists, only to annoy the homophobic out there!
 

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