The Algebra of Invariants of 3 × 3 Matrices Over a Field of Arbitrary Characteristic

Abstract

The least upper bound on degrees of elements of a minimal system of generators of the algebra of invariants of 3 × 3 matrices is found, and the nilpotency degree of a relatively free finitely generated algebra with the identity x ³ = 0 is established.

Key Words:

• Matrix invariants
• Polynomial identity
• Minimal generating system

Mathematics Subject Classification:

• 13A50
• 15A72
• 16R10
• 16R30

Acknowledgments

The author is grateful to A. N. Zubkov for helpful advices and constant attention, to G. A. Bazhenova for help with the translation. The author is also grateful to the referee whose comments considerably improved the paper. The author is supported by RFFI (grant 01.01.00674).

Notes

^#Communicated by I. Shestakov.