Let L be a Lie algebra over a field K. The dual Lie coalgebra Lº of L has been defined by W. Michaelis to be the sum of all good subspaces V of the dual space L* of L: V is good if tm(V) ⊂ V ⊗ V, where m is the multiplication of L. We show that Lº = tm-1(L* ⊗ L*) as in the associative case.
@article{urn:eudml:doc:41231,
title = {On the definition of the dual Lie coalgebra of a Lie algebra.},
journal = {Publicacions Matem\`atiques},
volume = {39},
year = {1995},
pages = {349-354},
mrnumber = {MR1370891},
zbl = {0857.16035},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41231}
}
Diarra, Bertin. On the definition of the dual Lie coalgebra of a Lie algebra.. Publicacions Matemàtiques, Tome 39 (1995) pp. 349-354. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41231/