Forms of higher degree permitting composition
Rings and Algebras
2007-05-23 v1
Abstract
Nondegenerate forms N of degree d on a unital nonassociative algebra A over a ring R which permit composition, i.e., satisfy N(1)=1 and N(xy)=N(x)N(y) for all x,y in A, are studied. These forms were first classified by Schafer over fields of characteristic 0 or >d. We investigate cubic and quartic nondegenerate forms which permit composition over certain rings and curves. Classes of highly degenerate cubic forms N over fields which permit composition are constructed.
Cite
@article{arxiv.0705.2522,
title = {Forms of higher degree permitting composition},
author = {S. Pumpluen},
journal= {arXiv preprint arXiv:0705.2522},
year = {2007}
}