ORIENTED INVOLUTIONS AND SKEW-SYMMETRIC ELEMENTS 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: JOURNAL OF ALGEBRA AND ITS APPLICATIONS; v. 12, n. 1 FEB 2013.
• Citações Web of Science: 1

Resumo

Let G be a group with involution {*} and sigma : G -> [+/- 1] a group homomorphism. The map \# that sends alpha = Sigma alpha(g)g in a group ring RG to alpha(\#) = Sigma sigma(g)alpha(g)g{*} is an involution of RG called an oriented group involution. An element alpha epsilon RG is symmetric if alpha(\#) = alpha and skew-symmetric if alpha(\#) = -alpha. The sets of symmetric and skew-symmetric elements have received a lot of attention in the special cases that {*} is the inverse map on G or sigma is identically 1, while the general case has been almost ignored. In this paper, we determine the conditions under which the set of elements that are skew-symmetric relative to a general oriented involution form a subring of RG. This is the sequel to another paper where the analogous problem for the symmetric elements was studied, with a small oversight that is corrected here. (AU)

• Processo FAPESP: 09/52665-0 - Grupos, anéis e álgebras: interações e aplicações
• Beneficiário: Francisco Cesar Polcino Milies
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 11/50046-1 - Edgar George Goodaire | University of Newfoundland - Canada
• Beneficiário: Francisco Cesar Polcino Milies
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional