Primitive Idempotents of Schur Rings
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- 作者：Andrew Misseldine (1)
- 关键词：Schur ring ; Cyclic group ; Primitive idempotent ; Group ring ; Wedderburn decomposition ; 20C05 ; 17C27 ; 16D70
- 刊名：Algebras and Representation Theory
- 出版年：2014
- 出版时间：October 2014
- 年：2014
- 卷：17
- 期：5
- 页码：1615-1634
- 全文大小：405 KB
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1. Department of Mathematics, Brigham Young University, Provo, UT, USA - ISSN：1572-9079
文摘
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 coefficients over a cyclic group, then these idempotents are always primitive and are spanned by the normal subgroups contained in S. Furthermore, a Wedderburn decomposition of Schur rings over cyclic groups is given. Some examples of Schur rings over non-cyclic groups will also be explored.