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- W2068175038 abstract "This paper is concerned with the structure of those space groups (or crystallographic groups) in n-dimensional Euclidean space for which the point groups are essential and generated by reflections. Recall [ 1 ] that a subgroup G in GL( V) is said to be essential if VG = (0). Those point groups are Weyl groups of root systems in the vector space [l]. The fundamental results are presented in Section 2. In a first step, we restrict our study to irreducible root systems. The principal result is stated in Theorem 2.6: in most cases the group H’(G, V/P(R)) is zero if the root system R is an irreducible one and the point group G is the Weyl group of R. Then, an easy consequence is given in Theorem 2.11: the same result holds even if the root system is a reducible one: we just have to forbid some types for its components. If /i is an invariant lattice such that Q(R) c /1 c P(R) the short exact sequence" @default.
- W2068175038 created "2016-06-24" @default.
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- W2068175038 date "1992-02-01" @default.
- W2068175038 modified "2023-10-01" @default.
- W2068175038 title "Classification of crystallographic groups associated with Coxeter groups" @default.
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- W2068175038 doi "https://doi.org/10.1016/0021-8693(92)90056-r" @default.
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