Involutions and Anticommutativity in Group Rings

Autor(es)

Goodaire, Edgar G. ^[1] ; Milies, Cesar Polcino ^[2]

Afiliação do(s) autor(es)

^[1] Mem Univ Newfoundland, St John, NF A1C 5S7 - Canada

^[2] Univ Sao Paulo, Inst Matemat & Estat, BR-05314970 Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES; v. 56, n. 2, p. 344-353, JUN 2013.
• Citações Web of Science: 4

Resumo

Let g -> g{*} denote an involution on a group G. For any (commutative, associative) ring R (with 1), {*} extends linearly to an involution of the group ring RG. An element alpha is an element of RG is symmetric if alpha{*} = alpha and skew-symmetric if alpha{*} = alpha. The skew-symmetric elements are closed under the Lie bracket, {[}alpha, beta] = alpha beta - beta alpha. In this paper, we investigate when this set is also closed under the ring product in RG. The symmetric elements are closed under the Jordan product, alpha o beta = alpha beta + beta alpha. Here, we determine when this product is trivial. These two problems are analogues of problems about the skew-symmetric and symmetric elements in group rings that have received a lot of attention. (AU)

• Processo FAPESP: 04/15319-3 - Interações entre grupo e anéis e aplicações
• Beneficiário: Francisco Cesar Polcino Milies
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 08/57553-3 - Edgar George Goodaire | Memorial University of Newfoundland - Canadá
• Beneficiário: Francisco Cesar Polcino Milies
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional