New Ternary Versions of Jordan Algebras

• 来源期刊: 代数集刊（英文版）
• 学科: 数学
• 关键词: identities ternary algebras Jordan algebras
• 年，卷（期）: 2001,（1）
• 页码范围: 11-24
• 页数: 14页
• 分类号: O1
• 语种: 英文

摘要

This paper determines the homogeneous identities of degree ≤ 7 satisfied by the ternary anti-commutator [a, b, c] :＝ abc+acb+bac+bca+cab+cba in triple systems satisfying either total associativity (abc)de ≡ a(bcd)e ≡ ab(cde)or partial associativity (abc)de + a(bcd)e + ab(cde) ≡ 0. These identities define new ternary versions of Jordan algebras different from Jordan triple systems.