Volume no :12, Issue no: 2, December (2014)

Journal of Algebra, Number Theory: Advances and Applications

A NOTE ON THE COMPUTATION OF SYMMETRIC POWERS OF HYPERBOLIC FORMS AND OF TRACE FORMS ON SYMBOL ALGEBRAS

Author's: Ronan Flatley
Pages: [91] - [110]
Received Date: October 1, 2014
Submitted by:

Abstract

Let K be a field with characteristic different from 2 and let S be a symbol algebra over K. We compute the symmetric powers of hyperbolic quadratic forms over K. Also, we compute the symmetric powers of the quadratic trace form of S. In both cases, we apply a generalized form of the Vandermonde convolution in the course of the computations.

Keywords

hyperbolic form, symmetric power, symbol algebra, trace form.