An Algebra of Pieces of Space — Hermann Grassmann to Gian Carlo Rota
by Henry Crapo, Les Moutons matheux, 34520 La Vacquerie, France
Invited Chapter in Book: From Combinatorics to Philosophy
Publisher: Springer US
ISBN: 978-0-387-88752-4 (Print) 978-0-387-88753-1 (Online)
Subject Collection Computer Science
SpringerLink Date Friday, July 24, 2009
We sketch the outlines of Gian Carlo Rota’s interaction with the ideas that Hermann Grassmann developed in his Ausdehnungslehre 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.