 
Summary: Journal of Algebra 298 (2006) 4157
www.elsevier.com/locate/jalgebra
Defining relations of invariants of two 3 × 3 matrices
Helmer Aslaksen a
, Vesselin Drensky b,,1
, Liliya Sadikova c
a Department of Mathematics, National University of Singapore, Singapore 117534, Singapore
b Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
c Fachgruppe Informatik, RWTH Aachen, 52056 Aachen, Germany
Received 12 May 2004
Available online 28 February 2006
Communicated by Michel Van den Bergh
Abstract
Over a field of characteristic 0, the algebra of invariants of several n × n matrices under simulta
neous conjugation by GLn is generated by traces of products of generic matrices. Teranishi, 1986,
found a minimal system of eleven generators of the algebra of invariants of two 3 × 3 matrices.
Nakamoto, 2002, obtained an explicit, but very complicated, defining relation for a similar system
of generators over Z. In this paper we have found another natural set of eleven generators of this
algebra of invariants over a field of characteristic 0 and have given the defining relation with respect
to this set. Our defining relation is much simpler than that of Nakamoto. The proof is based on easy
