Statements (29)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
|
| gptkbp:alsoKnownAs |
gptkb:U(1)
gptkb:unit_circle |
| gptkbp:containsElement |
e^{iθ} for θ in [0,2π)
|
| gptkbp:dimensions |
1
|
| gptkbp:fundamentalGroupOf |
circle S^1
|
| gptkbp:hasApplication |
Fourier analysis
quantum mechanics representation theory |
| gptkbp:hasSubgroup |
finite cyclic groups
|
| gptkbp:heldBy |
gptkb:topology
gptkb:Lie_group compact connected subgroup of complex numbers under multiplication abelian group of complex numbers of modulus 1 under multiplication simple example of a Lie group simple example of a compact group simple example of a topological group simple example of an abelian group |
| https://www.w3.org/2000/01/rdf-schema#label |
the circle group
|
| gptkbp:identityElement |
1
|
| gptkbp:isomorphicTo |
gptkb:SO(2)
real numbers modulo 1 under addition |
| gptkbp:universalCover |
gptkb:real_line_R
|
| gptkbp:bfsParent |
gptkb:the_ring_of_integers_Z
gptkb:locally_compact_Abelian_groups |
| gptkbp:bfsLayer |
7
|