Essential Dimension of Projective Orthogonal and Symplectic Groups of Small Degree

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.

Key Words:

• Central simple algebra
• Essential dimension
• Involution
• Projective orthogonal group
• Projective symplectic group

2010 Mathematics Subject Classification:

• 20G15
• 16W10

ACKNOWLEDGMENTS

I am grateful to A. Merkurjev for useful discussions. I am also grateful to J. P. Tignol, S. Garibaldi, and the anonymous referee for helpful comments.

Notes

Communicated by A. Wadsworth.