University Studies 4-Fall 2012-Suggested Projects from Seventh meeting 

Exercises 8,9,10 in the file below (Gradus ad Parnassum) concern verifying that certain linear transformations are derivations on the set of matrices. (Proofs of Propositions 5,6,7)

Exercises 11,12 in the file below (Gradus ad Parnassum) concern verifying that certain axioms are satisfied

Exercises 13,14 in the file below (Gradus ad Parnassum) concern verifying that certain linear transformations are derivations on certain abstract triple systems

Exercises 15,16,17,19 in the file below (Gradus ad Parnassum) concern contructions of triple systems from algebras

Exercise 18 in the file below (Gradus ad Parnassum) concerns constructing an algebra from a triple system.

Exercises 20,21 in the file below (Gradus ad Parnassum) concern the algebraic structure of the set of all derivations on an algebra or triple system.

At this point you should ignore Exercises 22-34 in the file below (Gradus ad Parnassum)

In response to a discussion after class, below are two pdf files of papers connecting triple systems to physics, and a reference connecting Jordan algebras to statistics.

Gradus ad Parnassum (Exercises 8-21) (pdffile)

Triple systems and Physics (Richard Kerner 2008) (pdffile)

Triple systems and Physics (Friedman-Russo 2001) (pdffile)

Statistical Applications of Jordan Algebras, by James D. Malley, Lecture notes in Statistics, 1994 (Ayala Science Library QA276 A1 L42 v.91)