An Algebra of Pieces of Space -- Hermann Grassmann to Gian Carlo Rota

Details An Algebra of Pieces of Space -- Hermann Grassmann to Gian Carlo Rota An Algebra of Pieces of Space -- Hermann Grassmann to Gian Carlo Rota

2009-04-21

arxiv.org/abs/0904.3349v1

Mathematics

History and Overview

28 pages

Scientific paper

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 Rota variously called 'Grassmann-Cayley algebra', or '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. The present paper was presented at the conference "The Digital Footprint of Gian-Carlo Rota: Marbles, Boxes and Philosophy" in Milano on 17 Feb 2009. It will appear in proceedings of that conference, to be published by Springer Verlag.

Affiliated with

Also associated with

No associations

Rating

An Algebra of Pieces of Space -- Hermann Grassmann to Gian Carlo Rota does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with An Algebra of Pieces of Space -- Hermann Grassmann to Gian Carlo Rota, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An Algebra of Pieces of Space -- Hermann Grassmann to Gian Carlo Rota will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-274514