Cauchy gave 1st example of a Lie algebra in 1847 & exterior product in 1853‽ I read in PDF pg. 5 of this that Cauchy gave the first example of a Lie algebra in 1847:

It also claims that he invented the exterior product in 1853.
Does anyone have references for this?
 A: Regarding Cauchy giving the first example of a Lie algebra, the following might, although I'm not exactly sure, be the reference, from: Lie, Sophus, and Georg Scheffers. Geometrie der berührungstransformationen. Leipzig: B.J. Teubner, 1896, p. 520.:

Im Jahre 1847 betonte Cauchy in einer kurzen Note dass der Begriff: w-dimensionaler Raum bei vielen analytischen Untersuchungen, namentlich inder Zahlentheorie, förderlich sei.
["In 1847 Cauchy stressed in a brief note that the term n-dimensional space in many analytical studies, especially in number theory, be beneficial."]

Cauchy, «Mémoire sur les lieux analytiques». Comptes rendus … de l’Académie des sciences 24 (1847), 885-887.

Regarding Cauchy giving the first example of an exterior product, this seems to be the reference, from “Grassmann, Hermann Günther.” In Complete Dictionary of Scientific Biography, 15:192–199. Detroit: Charles Scribner’s Sons, 2008.:
Cauchy, «Sur les clefs algébriques». Comptes rendus … de l’Académie des sciences 36 (1853), 70-76, 129-136
