2014
DOI: 10.1007/s10468-014-9466-y
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Primitive Idempotents of Schur Rings

Abstract: In this paper, we explore the nature of central idempotents of Schur rings over finite groups. We introduce the concept of a lattice Schur ring and explore properties of these kinds of Schur rings. In particular, the primitive, central idempotents of lattice Schur rings are completely determined. For a general Schur ring S, S contains a maximal lattice Schur ring, whose central, primitive idempotents form a system of pairwise orthogonal, central idempotents in S. We show that if S is a Schur ring with rational… Show more

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Cited by 4 publications
(1 citation statement)
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“…Thus, the main results of Leung and Man tell us that all Schur rings over finite cyclic groups are traditional. Note that the above mentioned non-Schurian example by Wielandt is non-traditional; see the last paragraph of the fourth page of [7].…”
Section: Introductionmentioning
confidence: 99%
“…Thus, the main results of Leung and Man tell us that all Schur rings over finite cyclic groups are traditional. Note that the above mentioned non-Schurian example by Wielandt is non-traditional; see the last paragraph of the fourth page of [7].…”
Section: Introductionmentioning
confidence: 99%