In mathematics, a covering group of a topological group H is a covering space G of H such that G is a topological group and the covering map p : G → H is a continuous group homomorphism. The map p is called the covering homomorphism. A frequently occurring case is a double covering group, a topological double cover in which H has index 2 in G; examples include the Spin groups, Pin groups, and metaplectic groups.
Roughly explained, saying that for example the metaplectic group Mp2n is a double cover of the symplectic group Sp2n means that there are always two elements in the metaplectic group representing one element in the symplectic group.
Read more about Covering Group: Properties, Group Structure On A Covering Space, Universal Covering Group, Lattice of Covering Groups, Lie Groups, Examples
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