login
a(n) is the dimension of the multilinear part of the free flexible Lie-admissible algebra with n generators.
1

%I #11 Feb 27 2024 09:45:16

%S 1,2,8,48,384,3841

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

%C The flexible identity is (x*y)*z + (z*y)*x = x*(y*z) + z*(y*x).

%C 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.

%C Flexible Lie-admissible algebras are algebras (possibly non-associative) satisfying those two identities.

%D Hyo Chul Myung, Flexible Lie-Admissible algebras (Thesis (Ph.D.)-Michigan State University), ProQuest LLC, Ann Arbor, MI, 1971.

%K nonn,hard,more

%O 1,2

%A _Paul Laubie_, Feb 26 2024