 
Summary: ö û
Comptes rendus de l'Acad´emie bulgare des Sciences
Tome 58, No 6, 2005
MATHEMATIQUES
Alg`ebre
DEFINING RELATIONS OF INVARIANTS
OF TWO 3 × 3 MATRICES1
H. Aslaksen, V. Drensky, L. Sadikova
(Submitted on March 23, 2005)
Abstract
Over a field of characteristic 0, Teranishi, 1986, found a minimal system of eleven
generators of the algebra of invariants of two 3 × 3 matrices under simultaneous
conjugation by GL3. Nakamoto, 2002, obtained the explicit, but very complicated
defining relation for a similar system of generators over Z. In this paper we give
another natural set of eleven generators of the algebra of invariants over a field of
characteristic 0 and the defining relation with respect to this generating set. Our
defining relation is much simpler than that of Nakamoto.
Key words: matrix invariants, defining relations, Hilbert series
2000 Mathematics Subject Classification: 16R30
Introduction. Let K be any field of characteristic 0 and let Cnd be the alge
