Concept
Topological group
Related concepts (52)
Solenoid (mathematics)
This page discusses a class of topological groups. For the wrapped loop of wire, see Solenoid. In mathematics, a solenoid is a compact connected topological space (i.e. a continuum) that may be obtained as the inverse limit of an inverse system of topological groups and continuous homomorphisms where each is a circle and fi is the map that uniformly wraps the circle for times () around the circle . This construction can be carried out geometrically in the three-dimensional Euclidean space R3.
Induced representation
In group theory, the induced representation is a representation of a group, G, which is constructed using a known representation of a subgroup H. Given a representation of H, the induced representation is, in a sense, the "most general" representation of G that extends the given one. Since it is often easier to find representations of the smaller group H than of G, the operation of forming induced representations is an important tool to construct new representations.