On the decomposition of metabolic involutions

TL;DR

This paper investigates the conditions under which metabolic involutions and skew-symmetric elements in central simple algebras are contained within invariant quaternion subalgebras, advancing understanding of algebraic involution structures.

Contribution

It introduces new criteria for embedding metabolic involutions and skew-symmetric elements into invariant quaternion subalgebras in central simple algebras.

Findings

Characterization of metabolic involutions within quaternion subalgebras

Conditions for skew-symmetric elements with squares in the base field

Insights into algebraic structures with involution

Abstract

The problem of whether a metabolic idempotent of a central simple algebra with involution is contained in an invariant quaternion subalgebra is investigated. As an application, the similar problem is studied for skew-symmetric elements whose squares lie in the square of the underlying field.