Notes on de Sitter space
نویسندگان
چکیده
The Lorentz n–group is the group of “isometries” (transformations preserving the inner product) of Minkowski space, fixing 0, and preserving the time direction. This implies that a Lorentz transformation is an linear isomorphism of Rn as a vector space. If, in addition to preserving the time direction, we also preserve space orientation then the group can be denoted SO(1, n − 1). Notice that a Lorentz transformation which preserves the x0 –axis is an othogonal transformation of the perpendicular (n−1)–space, thus SO(n− 1) is a subgroup of SO(1, n− 1) and we refer to elements of this subgroup as (Euclidean) rotations about the x0 –axis.
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