✦ LIBER ✦
Identities for Generalized Lie and Jordan Products on Totally Associative Triple Systems
✍ Scribed by Murray Bremner; Irvin Hentzel
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 110 KB
- Volume
- 231
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
✦ Synopsis
We determine the identities of degree F 9 satisfied by the new ternary opera-Ž . tions abc q bca q cab q acb q bac q cba symmetric sum , abc q bca q cab y Ž . Ž . acb y bac y cba alternating sum , and abc q bca q cab cyclic sum on every Ž . Ž . triple system satisfying the total associativity identities abc de ' a bcd e ' Ž . ab cde . These new operations are ternary analogs of the Lie and Jordan products. The identities they satisfy may be regarded as ternary versions of the Jacobi and Jordan identities.