Associators and Commutators in Alternative Algebras

Autor(es)

Kleinfeld, E. ; Shestakov, I. P. ^{[1, 2]}

Afiliação do(s) autor(es)

^[1] Sobolev Inst Math, Pr Akad Koptyuga 4, Novosibirsk 630090 - Russia

^[2] Univ Sao Paulo, BR-05315970 Sao Paulo, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Algebra and Logic; v. 58, n. 4, p. 322-326, SEP 2019.
• Citações Web of Science: 0

Resumo

It is proved that in a unital alternative algebra A of characteristic not equal 2, the associator (a, b, c) and the Kleinfeld function f(a, b, c, d) never assume the value 1 for any elements a, b, c, d is an element of A. Moreover, if A is nonassociative, then no commutator {[}a, b] can be equal to 1. As a consequence, there do not exist algebraically closed alternative algebras. The restriction on the characteristic is essential, as exemplified by the Cayley-Dickson algebra over a field of characteristic 2. (AU)

• Processo FAPESP: 14/09310-5 - Estruturas algébricas e suas representações
• Beneficiário: Vyacheslav Futorny
• Modalidade de apoio: Auxílio à Pesquisa - Temático