Geometric Algebra (book)

In 1962 Algèbre Géométrique, a translation into French by Michel Lazard, was published by Gauthier-Villars, and reprinted in 1996.

[1] In 1969 a translation into Russian was published in Moscow by Nauka[2] Long anticipated as the sequel to Moderne Algebra (1930), which Bartel van der Waerden published as his version of notes taken in a course with Artin, Geometric Algebra is a research monograph suitable for graduate students studying mathematics.

To suggest the role of incidence in geometry, a dilation is specified by this property: "If l′ is the line parallel to P + Q which passes through P′, then Q′ lies on l′."

Conversely, there is an affine geometry based on any given skew field k. Axioms 4a and 4b are equivalent to Desargues' theorem.

It begins with metric structures on vector spaces before defining symplectic and orthogonal geometry and describing their common and special features.

Alice T. Schafer wrote "Mathematicians will find on many pages ample evidence of the author’s ability to penetrate a subject and to present material in a particularly elegant manner."

She notes the overlap between Artin's text and Baer's Linear Algebra and Projective Geometry or Dieudonné's La Géometrie des Groupes Classique.