Essential dimension of projective orthogonal and symplectic groups of small degree

TL;DR

This paper determines the essential dimension of certain algebraic groups related to central simple algebras with involutions of small index, providing new insights into their structural properties.

Contribution

It introduces new calculations of the essential dimension for projective and symplectic groups of small degree based on structural theorems for simple algebras with involutions.

Findings

Essential dimension of projective groups of small degree computed.

Essential dimension of symplectic groups of small degree determined.

Structural theorems for simple algebras with involutions underpin the results.

Abstract

In this paper, we study the essential dimension of classes of central simple algebras with involutions of index less or equal to 4. Using structural theorems for simple algebras with involutions, we obtain the essential dimension of projective and symplectic groups of small degree.