Classification of Quadratic Homogeneous Automorphisms in Dimension Five

Abstract

In this paper, we present a classification of quadratic homogeneous automorphisms in dimension 5 up to linear conjugation. As a consequence, we give an affirmative answer to the Rusek Conjecture in dimension 5.

Key Words:

• Quadratic homogeneous maps
• Rusek Conjecture
• Tame automorphisms

2010 Mathematics Subject Classification:

• 14R10

ACKNOWLEDGMENTS

The author wishes to thank the referee for his suggestions and thank Professor Jiping Zhang and Professor Xiankun Du for their help and encouragement.

This work was supported by the Basic Scientific Research Fund of Ministry of Education of China, “985 Project” and “211 Project” of Jilin University.

Notes

Communicated by J.-T. Yu.