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osu1187185559.pdf (220.63 KB)
ETD Abstract Container
Abstract Header
An infinite family of anticommutative algebras with a cubic form
Author Info
Schoenecker, Kevin J
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1187185559
Abstract Details
Year and Degree
2007, Doctor of Philosophy, Ohio State University, Mathematics.
Abstract
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
Committee
Bostwick Wyman (Advisor)
Subject Headings
Mathematics
Keywords
anticommutative algebra
;
noncommutative Jordan algebra
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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)
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Document number:
osu1187185559
Download Count:
701
Copyright Info
© 2007, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.