منابع مشابه
Symmetric Units and Group Identities in Group Algebras. I
We describe those group algebras over fields of characteristic different from 2 whose units symmetric with respect to the classical involution, satisfy some group identity.
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Let U(KG) be the group of units of the group ring KG of the group G over a commutative ring K . The anti-automorphism g 7→ g of G can be extended linearly to an anti-automorphism a 7→ a∗ of KG . Let S∗(KG) = {x ∈ U(KG) | x∗ = x} be the set of all symmetric units of U(KG) . We consider the following question: for which groups G and commutative rings K it is true that S∗(KG) is a subgroup in U(KG...
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Let p be a prime, G a locally finite p -group, K a commutative ring of characteristic p . The anti-automorphism g 7→ g of G extends linearly to an anti-automorphism a 7→ a∗ of KG . An element a of KG is called symmetric if a∗ = a . In this paper we answer the question: for which G and K do the symmetric units of KG form a multiplicative group. Let G be a group, K a commutative ring (with 1), an...
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We give a simple proof of the equivalence of the matrix unit formulas for the symmetric group provided by Murphy’s construction and by the fusion procedure due to Cherednik. 1 Young basis Let us fix some notation and recall some well known facts about the representations of the symmetric group Sn; see e.g. [6]. We write a partition λ as a sequence λ = (λ1, . . . , λl) of integers such that λ1 >...
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Let Sn denote the symmetric group on n symbols. When F has characteristic zero or greater than n, the group algebra FSn is a direct sum of p(n) matrix algebras over F, where p(n) is the number of partitions of n. We present an efficient method due to J. M. Clifton (1981) that calculates the matrix associated to each element of Sn, for each partition of n. In 1950, A. I. Malcev and W. Specht ind...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2009
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2009.06.025