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Zbl 1100.16019
Aslaksen, Helmer; Drensky, Vesselin; Sadikova, Liliya
Defining relations of invariants of two $3\times 3$ matrices. (English)
[J] J. Algebra 298, No. 1, 41-57 (2006). ISSN 0021-8693

All algebras considered in the paper are over a fixed field of characteristic 0. Consider two generic $3\times 3$ matrices. The conjugation by elements of $\text{GL}_3$ defines an action of this group on the commutative polynomial algebra in 18 variables (the entries of the two generic matrices). Let $C$ be the corresponding algebra of invariants. It is well known that $C$ is generated by traces of products of the two given matrices.\par The main aim of the paper under review is the description of the generators of $C$ and the relations among them. The system constructed consists of 11 elements with one relation. The system of generators is quite natural and the relation has a very simple form.\par It is worth mentioning that the authors do not ``hide'' anything: the last Section 2 of the paper describes the approach followed to discover the relation among the generators. The reviewer has found it quite interesting and well timed.
[Plamen Koshlukov (Campinas)]

MSC 2000:: *16R30 Trace rings and invariant theory (assoc. rings and algebras)
15A72 Vector and tensor algebra

Keywords: matrix invariants; generating sets of invariants; relations among invariants; minimal generating systems; generic matrices

Cited in: Zbl 1142.16009

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