The ring of invariants of pairs of 3 × 3 matrices

García Martínez, Xabier; Normatov, Zafar; Turdibaev, Rustam

doi:10.1016/j.jalgebra.2022.04.001

García Martínez, Xabier

; Normatov, Zafar; Turdibaev, Rustam

DATE: 2022-08-01

UNIVERSAL IDENTIFIER: http://hdl.handle.net/11093/7895

EDITED VERSION: https://linkinghub.elsevier.com/retrieve/pii/S0021869322001478

UNESCO SUBJECT: 12 Matemáticas ; 1201 Álgebra

DOCUMENT TYPE: article

ABSTRACT

The defining relation on the minimal set of generators of the invariants of pairs of matrices of degree three has been established by Nakamoto. Furthermore, it has been simplified with another minimal set of generators by Aslaksen, Drensky and Sadikova using methods coming from representation theory. This work is devoted to obtain this defining relation in a completely different and novel way. We use the Poisson algebra structure on the ring of invariants of pairs of matrices to do so.

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