Hyperbolicity of orthogonal involutions

TL;DR

This paper proves that non-hyperbolic orthogonal involutions on central simple algebras stay non-hyperbolic over some splitting field, highlighting stability properties of involutions in algebraic structures.

Contribution

It establishes a new result about the persistence of non-hyperbolicity of orthogonal involutions over splitting fields, advancing understanding in algebraic involution theory.

Findings

Non-hyperbolic involutions remain non-hyperbolic over some splitting field.

The result applies to central simple algebras in characteristic not 2.

Provides insights into the behavior of involutions under field extensions.

Abstract

We show that a non-hyperbolic orthogonal involution on a central simple algebra over a field of characteristic different from 2 remains non-hyperbolic over some splitting field of the algebra.