University of Cambridge > > DPMMS Pure Maths Seminar > Affine algebra

Affine algebra

Add to your list(s) Download to your calendar using vCal

  • UserVaughan Pratt (Stanford University)
  • ClockThursday 25 September 2008, 14:15-16:00
  • HouseMR12.

If you have a question about this talk, please contact Helen Innes.

We axiomatize affine algebra equationally in terms of the geometric primitives of reflection and centroid. This reduces the usual three-stage algebraic development of affine geometry (fields then vector spaces then torsors) to a single stage. The expansion of this variety with a lawless constant is equivalent to vector spaces over the rationals (or complex rationals when further expanded with quarter-turn rotation). Completion to the continuum is accomplished entirely within this framework via a notion of convergence of pairs of point sets constituting a partial equivalence relation, with Cauchy sets defined as those sets that converge with themselves. The additive fragment based on reflection, whose models we call groves, is of independent interest as a weak generalization of heaps/herds as an affine counterpart of abelian groups.

This talk is part of the DPMMS Pure Maths Seminar series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.


© 2006-2024, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity