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

Invited Chapter
  • Henry Crapo

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.

Keywords

Hopf Algebra Invariant Theory Geometric Algebra Geometric Product Projective Subspace 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Henry Crapo
    • 1
  1. 1.Centre de Recherche “Les Moutons matheux”ParisFrance

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