Search ETDs:
An infinite family of anticommutative algebras with a cubic form
Schoenecker, Kevin J

2007, Doctor of Philosophy, Ohio State University, Mathematics.
A noncommutative Jordan Algebra, J, of degree two can be constructed from an anticommutative algebra S that has a symmetric associative bilinear form. If additional conditions are put on the algebra S, information about the derivations and automorphisms of J can be obtained. If S is a n+1 dimensional algebra, and T is a nonsingular linear transformation on S, it is of interest to know what multiplications and what nondegenerate symmetric associative bilinear forms, can be put on S so that T(T(x)T(y))=xy for all x,y,z in S, and T is equal to its adjoint. If T has only one Jordan block the question is answered, in the form of conditions that must be satisfied on the multiplication constants. It is shown such algebras exist for all n and it is shown how to obtain the multiplication tables
Bostwick Wyman (Advisor)

Recommended Citations

Hide/Show APA Citation

Schoenecker, K. (2007). An infinite family of anticommutative algebras with a cubic form. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

Hide/Show MLA Citation

Schoenecker, Kevin. "An infinite family of anticommutative algebras with a cubic form." Electronic Thesis or Dissertation. Ohio State University, 2007. OhioLINK Electronic Theses and Dissertations Center. 26 Sep 2017.

Hide/Show Chicago Citation

Schoenecker, Kevin "An infinite family of anticommutative algebras with a cubic form." Electronic Thesis or Dissertation. Ohio State University, 2007. https://etd.ohiolink.edu/

Files

osu1187185559.pdf (220.63 KB) View|Download