There seems to be a problem in the literature about the definition of the 'standard' coboundary on the 'Cartan-Chevalley-Eilenberg' algebra - the problem is the signs!

Where/when did things go wrong? And what's the best way to reference so the next generation learns only the correct signs?

with more precision: the usual C-E coboundary has two summations - for the module structure and for the algebra each is separately correct in all references but some have the sum squaring to zero and others not -i.e. wrong relative sign for the two summations

Here's the original reference: Chevalley, Claude; Eilenberg, Samuel (1948), "Cohomology Theory of Lie Groups and Lie Algebras", Transactions of the American Mathematical Society (Providence, R.I.: American Mathematical Society) 63 (1): 85–124,

and some others that may or may not copy the first Hilton, P. J.; Stammbach, U. (1997), A course in homological algebra, Graduate Texts in Mathematics, 4 (2nd ed.), Berlin, New York: Springer-Verlag, ISBN 978-0-387-94823-2, MR 1438546 Knapp, Anthony W. (1988), Lie groups, Lie algebras, and cohomology, Mathematical Notes, 34, Princeton University Press, ISBN 978-0-691-08498-5, MR 938524

The signs are correct (I believe) in