Abstract
We sketch the outlines of Gian Carlo Rota’s interaction with the ideas that Hermann Grassmann developed in his Ausdehnungslehre[13, 15] of 1844 and 1862, as adapted and explained by Giuseppe Peano in 1888. This leads us past what Gian Carlo variously called Grassmann-Cayley algebra and Peano spaces to the Whitney algebra of a matroid, and finally to a resolution of the question “What, really, was Grassmann’s regressive product?”. This final question is the subject of ongoing joint work with Andrea Brini, Francesco Regonati, and William Schmitt.
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Crapo, H. (2009). An Algebra of Pieces of Space — Hermann Grassmann to Gian Carlo Rota. In: Damiani, E., D’Antona, O., Marra, V., Palombi, F. (eds) From Combinatorics to Philosophy. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-88753-1_5
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