Triple

Target class: Lie group action
Context triple: [Fuchsian group, instanceOf, Lie group action]

• A. simple Lie group
  A simple Lie group is a connected non-abelian Lie group whose Lie algebra is simple, meaning it has no nontrivial proper ideals and is not a direct sum of smaller Lie algebras.
• B. non-compact Lie group
  A non-compact Lie group is a Lie group whose underlying topological space is not compact, meaning it is a smooth group manifold that is unbounded or not closed in the sense of compactness.
• C. topological group chosen
  A topological group is a group equipped with a topology such that the group operation and inversion are continuous maps with respect to that topology.
• D. pseudogroup
  A pseudogroup is a collection of local homeomorphisms (or diffeomorphisms) on a topological space that is closed under composition, inversion, restriction to open subsets, and gluing of compatible local maps, generalizing the notion of a group action to local symmetries.
• E. representation of a group
  A representation of a group is a homomorphism from that group into the group of linear transformations of a vector space, allowing the group’s abstract elements to be studied via concrete matrices or operators.
• F. None of above.