arXiv subjects
Publications and source records attributed to S. Pumpluen.
Let F be a field of characteristic 0 or greater than d. Scharlau's norm principle holds for separable field extensions K over F, for certain forms $ϕ$ of degree d over F which permit composition.
Both a general and a diagonal u-invariant for forms of higher degree are defined, generalizing the u-invariant of quadratic forms. Both old and new results on these invariants are collected.
Several notions of multiplicativity are introduced for forms of degree $d\geq 3$ over a field of characteristic 0 or greater than d. Examples of multiplicative and strongly multiplicative forms of higher degree are given. Conditions restricting the structure of a strongly multiplicative form are found.
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.
Let R be a ring. A construction method for flexible quadratic algebras with scalar involution over R is presented which unifies various classical constructions in the literature, in particular those to construct composition algebras.
A simple sufficient condition for certain cyclic algebras of odd degree d to be split is presented. It employs certain binary forms of degree d and the values they represent. A similar sufficient condition for certain Albert algebras not to be division algebras is found as well.