The structure of the invariant ring of two matrices of degree 3

DOI10.1016/S0022-4049(01)00004-4zbMath1001.15022OpenAlexW2026384431MaRDI QIDQ5956874

Kazunori Nakamoto

Publication date: 10 December 2002

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0022-4049(01)00004-4

zbMATH Keywords

generatorsinvariant ringmatrices of degree 3

Mathematics Subject Classification ID

Vector and tensor algebra, theory of invariants (15A72) Representations of quivers and partially ordered sets (16G20) Vector bundles on curves and their moduli (14H60)

Related Items (14)

Poisson algebra structure on the invariants of pairs of matrices of degree three ⋮ Generators, relations and symmetries in pairs of \(3\times 3\) unimodular matrices ⋮ The ring of invariants of pairs of \(3 \times 3\) matrices ⋮ Defining relations of the noncommutative trace algebra of two \(3\times 3\) matrices. ⋮ Generating sets for coordinate rings of character varieties ⋮ Defining relation for semi-invariants of three by three matrix triples ⋮ Poisson structure on the invariants of pairs of matrices ⋮ Defining relations of minimal degree of the trace algebra of \(3\times 3\) matrices. ⋮ Minimal affine coordinates for SL\((3,\mathbb C)\) character varieties of free groups ⋮ Defining relations of invariants of two \(3\times 3\) matrices. ⋮ Indecomposable Invariants of Quivers for Dimension (2,…,2) and Maximal Paths ⋮ DEFINING RELATIONS OF LOW DEGREE OF INVARIANTS OF TWO 4 × 4 MATRICES ⋮ Poisson geometry of 𝑆𝐿(3,ℂ)-character varieties relative to a surface with boundary ⋮ On minimal generating systems for matrixO(3)-invariants

Cites Work

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• Rings of Fricke characters and automorphism groups of free groups
• Invariants of several matrices
• The invariant theory of \(n\times n\) matrices
• On the character variety of group representations in \(\text{SL}(2,\mathbb{C})\) and \(\text{PSL}(2,\mathbb{C})\)
• Representation varieties and character varieties
• Characters of free groups represented in the two‐dimensional special linear group
• On the coordinate rings of quiver varieties associated to extended Dynkin diagrams

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