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- W768852188 abstract "We investigate the possibility of semigroup extensions of the isometry group of an identification space, in particular, of a compactified spacetime arising from an identification map $p: RR^n_t to RR^n_t / Gamma$, where $RR^n_t$ is a flat pseudo-Euclidean covering space and $Gamma$ is a discrete group of primitive lattice translations on this space. We show that the conditions under which such an extension is possible are related to the index of the metric on the subvector space spanned by the lattice vectors: If this restricted metric is Euclidean, no extensions are possible. Furthermore, we provide an explicit example of a semigroup extension of the isometry group of the identification space obtained by compactifying a Lorentzian spacetime over a lattice which contains a lightlike basis vector. The extension of the isometry group is shown to be isomorphic to the semigroup $(ZZ^{times},cdot)$, i.e. the set of nonzero integers with multiplication as composition and 1 as unit element. A theorem is proven which illustrates that such an extension is obstructed whenever the metric on the covering spacetime is Euclidean." @default.
- W768852188 created "2016-06-24" @default.
- W768852188 creator A5018155353 @default.
- W768852188 date "1998-10-19" @default.
- W768852188 modified "2023-09-24" @default.
- W768852188 title "Semigroup extensions of isometry groups of flat spacetimes compactified over lightlike lattices" @default.
- W768852188 hasPublicationYear "1998" @default.
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