OFFSET
1,2
COMMENTS
The flexible identity is (x*y)*z + (z*y)*x = x*(y*z) + z*(y*x).
The Lie-admissible identity is (x*y)*z - x*(y*z) + z*(y*x) - (z*y)*x + y*(x*z) - (y*x)*z = (x*z)*y - x*(z*y) + y*(z*x) - (y*z)*x + z*(x*y) - (z*x)*y.
Flexible Lie-admissible algebras are algebras (possibly non-associative) satisfying those two identities.
REFERENCES
Hyo Chul Myung, Flexible Lie-Admissible algebras (Thesis (Ph.D.)-Michigan State University), ProQuest LLC, Ann Arbor, MI, 1971.
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Paul Laubie, Feb 26 2024
STATUS
approved