منابع مشابه
Uniform Distribution and the Schur Subgroup
In this paper we continue the investigation into the group of algebras with uniformly distributed invariants U(K), and its relation to the Schur subgroup, undertaken in [9]. The notation is the same as in [9]. In the first section we investigate the index 1 U(K), : S(K), 1 where q is an odd prime. We obtain [9, Theorem 2.71 as a special case of Theorem 1.2, wherein we obtain that the above inde...
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If N is a nontrivial proper normal subgroup of a finite group G then N and G/N are smaller than G. While it is false that G can be completely reconstructed from knowledge of N and G/N (see Example 1.1 below), it is nevertheless a standard technique in finite group theory to prove theorems about finite groups by induction on the size of the group and thereby use information about the smaller gro...
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Let K be an abelian extension of the rationals. Let S(K) be the Schur group of K and let CC(K) be the subgroup of S(K) generated by classes containing cyclic cyclotomic algebras. We characterize when CC(K) has finite index in S(K) in terms of the relative position of K in the lattice of cyclotomic extensions of the rationals.
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Schur duality decomposes many copies of a quantum state into subspaces labeled by partitions, a decomposition with applications throughout quantum information theory. Here we consider applying Schur duality to the problem of distinguishing coset states in the standard approach to the hidden subgroup problem. We observe that simply measuring the partition (a procedure we call weak Schur sampling...
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Large scale optimization of systems governed by partial differential equations (PDEs) is a frontier problem in scientific computation. The state-of-the-art for such problems is reduced quasi-Newton sequential quadratic programming (SQP) methods. These methods take full advantage of existing PDE solver technology and parallelize well. However, their algorithmic scalability is questionable; for c...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1972
ISSN: 0021-8693
DOI: 10.1016/0021-8693(72)90154-8