Note on co-split Lie algebras

Abstract

It is proved that, any finite dimensional complex Lie algebra L = [L, L], hence, over a field of characteristic zero, any finite dimensional Lie algebra L = [L, L] possessing a basis with complex structure constants, should be a weak co-split Lie algebra. A class of non-semi-simple co-split Lie algebras is given.

Keywords

Co-split / Casimir operator / Killing form

References

[1] Xia L. M., Hu N. H.. Introduction to co-split Lie algebras. Algebr. Repres. Theory, 2011, 14(1): 191-199

[2] Farnsteiner R.. Lie algebras with a coalgebra splitting. Algebr. Repres. Theory, 2011, 14(1): 87-96