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An infinite family of anticommutative algebras with a cubic form

Schoenecker, Kevin J
http://rave.ohiolink.edu/etdc/view?acc_num=osu1187185559

Abstract Details

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)
Mathematics
anticommutative algebra; noncommutative Jordan algebra

Recommended Citations

Citations

  • Schoenecker, K. J. (2007). An infinite family of anticommutative algebras with a cubic form [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1187185559

    APA Style (7th edition)

  • Schoenecker, Kevin. An infinite family of anticommutative algebras with a cubic form. 2007. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1187185559.

    MLA Style (8th edition)

  • Schoenecker, Kevin. "An infinite family of anticommutative algebras with a cubic form." Doctoral dissertation, Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=osu1187185559

    Chicago Manual of Style (17th edition)

osu1187185559
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© 2007, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.