Trace Forms of Symbol Algebras

TL;DR

This paper computes the trace form of symbol algebras and demonstrates how it can be used to determine their division algebra status, also exploring the exterior powers of the trace form.

Contribution

It provides explicit calculations of the trace form for symbol algebras and links these forms to their division algebra properties, including exterior powers.

Findings

Trace form of symbol algebra computed

Criterion for division algebra determined from trace form

Exterior powers of the trace form explicitly calculated

Abstract

Let S be a symbol algebra. The trace form of S is computed and it is shown how this form can be used to determine whether S is a division algebra or not. In addition, the exterior powers of the trace form of S are computed.