A370677 a(n) is the dimension of the multilinear part of the free flexible Lie-admissible algebra with n generators.

1, 2, 8, 48, 384, 3841

Offset: 1

Author

Paul Laubie, Feb 26 2024

Keywords

• nonn
• hard
• more

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.