On a Certain Complex Related to the Notion of Hyperdeterminant

The notion of determinant slowly emerged during a period of one hundred and twenty years, from the pioneering work of Leibniz to the celebrated 1812 memoir of Cauchy, which contained all the fundamental properties. The subsequent forty years were devoted to a further systematization of the theory, so that its importance came to be recognized by the mathematical community. A sign of that recognition was the appearance of the first complete treatise on determinants, written by Brioschi (Pavia 1854, French and German translations 1856).1