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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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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We determine the commutative Schur rings over S6 that contain the sum of all the transpositions in S6. There are eight such types (up to conjugacy), of which four have the set of all the transpositions as a principal set of the Schur ring. 2010 MSC: 20C05, 20F55
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1972
ISSN: 0021-8693
DOI: 10.1016/0021-8693(72)90155-x