Local group representations (Q1176114)

The usual (global) group representations assign linear operators in a Hilbert (Banach) space to all group elements. In contrast, the local group representations, considered here, make this assignment for a subset of group elements in a neighborhood of the identity. For it maybe that for some physical systems symmetries do not hold for ``large'' group elements. In that case, physicists use Lie algebra representations. But in general these do not extend or come from group representations. Here local group representations are defined as a sheaf over \(G\) with domain \(D\) dense in a Banach space \(B\), as continuous and \(G\)-homogeneous mappings; their properties and extensions are studied.