Article

Nuclear Elements of Degree 6 in the Free Alternative Algebra

Experimental Mathematics
Document Type

Article
Disciplines

- Algebra and
- Mathematics

Publication Date

1-1-2008
Abstract

We construct five new elements of degree 6 in the nucleus of the free alternative algebra. We use the representation theory of the symmetric group to locate the elements. We use the computer algebra system ALBERT and an extension of ALBERT to express the elements in compact form and to show that these new elements are not a consequence of the known degree-5 elements in the nucleus. We prove that these five new elements and four known elements form a basis for the subspace of nuclear elements of degree 6. Our calculations are done using modular arithmetic to save memory and time. The calculations can be done in characteristic zero or any prime greater than 6, and similar results are expected. We generated the nuclear elements using prime 103. We check our answer using five other primes.
Copyright Owner

Taylor & Francis
Copyright Date

2008
Language

en
File Format

application/pdf
Citation Information

Irvin R. Hentzel and L. A. Peresi. "Nuclear Elements of Degree 6 in the Free Alternative Algebra" *Experimental Mathematics*Vol. 17 Iss. 2 (2008) p. 245 - 255

Available at: http://works.bepress.com/irvin-hentzel/19/

This article is published as Hentzel, I. R., and L. A. Peresi. "Nuclear Elements of Degree 6 in the Free Alternative Algebra."

Experimental Mathematics17, no. 2 (2008): 245-255. Posted with permission.