Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0704.2410

The Invariant Ring of Triples of 3x3 Matrices over a Field of Arbitrary Characteristic

A. A. Lopatin
View original source ↗Read source document ↗Export metadata ↓

Abstract

Let R_{n,d} be the ring of invariants of d-tuples of n x n matrices under the simultaneous conjugation action of the general linear group. A minimal generating system and a homogeneous system of parameters for R_{3,3} are determined. Homogeneous systems of parameters for R_{3,2}, R_{4,2} are also pointed out.

Explore related subjects

math.RAmath.AC

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

A. A. Lopatin. 2007-04-18. The Invariant Ring of Triples of 3x3 Matrices over a Field of Arbitrary Characteristic. https://arxiv.org/abs/0704.2410

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Multilinear nilalgebras and the Jacobian theorem

If a symmetric multilinear algebra is weakly nil, then it is Engel. This result may be regarded as an infinite-dimensional analogue of the well-known Jacobian theorem, which states that if a polynomial mapping has a polynomial inverse, then its Jacobian matrix is invertible. This refines a theorem of Gerstenhaber and partially answers a question posed by Dotsenko.

math.RA↗
arXiv2026

Local (Anti-)Superderivations on Nilpotent Lie Superalgebras

In this paper, we study local superderivations and local anti-superderivations of finite-dimensional nilpotent Lie superalgebras over a field $\mathbb F$ with $\operatorname{char}\mathbb F\neq2$. First, we prove that every finite-dimensional two-step nilpotent Lie superalgebra admits pure local superderivations and pure local anti-superderivations (namely, local (anti-)superderivations that are not (anti-)superderivations). For nilpotent Lie superalgebras of nilpotency index greater than two, we establish sufficient conditions for the existence of pure local superderivations and pure local anti-superderivations. In particular, we prove that every three-step nilpotent Lie superalgebra admits a pure local superderivation.

math.RA↗