Involutions of RA Loops

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. 52, n. 2, p. 245-256, JUN 2009.
• Citações Web of Science: 0

Resumo

Let L be an RA loop, that is, a loop whose loop ring over any coefficient ring R is an alternative, but not associative, ring. Let l bar right arrow l(theta) denote an involution on L and extend it linearly to the loop ring RL. An element alpha is an element of RL is symmetric if alpha(theta) = alpha and skew-symmetric if alpha(theta) = -alpha. In this paper, we show that there exists an involution making the symmetric elements of RL commute if and only if the characteristic of R is 2 or theta is the canonical involution on L, and an involution making the skew-symmetric elements of RL commute if and only if the characteristic of R is 2 or 4. (AU)

• Processo FAPESP: 05/60411-8 - Edgar George Goodaire | Memorial University of Newfoundland - Canadá
• Beneficiário: Francisco Cesar Polcino Milies
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional