Images of polynomials on superalgebras and commutators on algebras
The structure problems of Zinbiel-Lie and Novikov-Jordan algebras
Lie and Jordan algebras, their representations and generalizations
| Full text | |
| Author(s): |
Kleinfeld, E.
;
Shestakov, I. P.
[1, 2]
Total Authors: 2
|
| Affiliation: | [1] Sobolev Inst Math, Pr Akad Koptyuga 4, Novosibirsk 630090 - Russia
[2] Univ Sao Paulo, BR-05315970 Sao Paulo, SP - Brazil
Total Affiliations: 2
|
| Document type: | Journal article |
| Source: | Algebra and Logic; v. 58, n. 4, p. 322-326, SEP 2019. |
| Web of Science Citations: | 0 |
| Abstract | |
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) | |
| FAPESP's process: | 14/09310-5 - Algebraic structures and their representations |
| Grantee: | Vyacheslav Futorny |
| Support Opportunities: | Research Projects - Thematic Grants |