Minimal affine coordinates for SL\((3,\mathbb C)\) character varieties of free groups

DOI10.1016/j.jalgebra.2008.06.031zbMath1157.14030arXiv0709.4403OpenAlexW2126528082MaRDI QIDQ958997

Sean Lawton

Publication date: 10 December 2008

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0709.4403

zbMATH Keywords

free groupcharacter varietyminimal generators

Mathematics Subject Classification ID

Geometric invariant theory (14L24)

Related Items (13)

Line operators in theories of class \( \mathcal{S} \), quantized moduli space of flat connections, and Toda field theory ⋮ Varieties of characters ⋮ Generating sets for coordinate rings of character varieties ⋮ Algebraic independence in \(\mathrm{SL}(3, \mathbb C)\) character varieties of free groups ⋮ Motive of the \(\mathrm{SL}_4\)-character variety of torus knots ⋮ Invariants of pairs in 𝑆𝐿(4,ℂ) and 𝕊𝕌(3,1) ⋮ Representation varieties of twisted Hopf links ⋮ Computing SL\((2,\mathbb{C})\) central functions with spin networks ⋮ Rank 1 character varieties of finitely presented groups ⋮ Conjugation orbits of loxodromic pairs in \(\mathrm{SU}(n, 1)\) ⋮ Special elliptic isometries, relative \(\mathrm{SU}(2,1)\)-character varieties, and bendings ⋮ Character varieties ⋮ On conjugation orbits of semisimple pairs in rank one

Cites Work

• Substitutions in dynamics, arithmetics and combinatorics
• The invariants of six symmetric \(3 \times 3\) matrices
• The theory of matrix polynomials and its application to the mechanics of isotropic continua
• Finite integrity bases for five or fewer symmetric 3 \(\times\) 3 matrices
• Further results in the theory of matrix polynomials
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• Defining relations for the algebra of invariants of \(2\times 2\) matrices
• Polynomial identity rings.
• Generators, relations and symmetries in pairs of \(3\times 3\) unimodular matrices
• Defining relations of invariants of two \(3\times 3\) matrices.
• Invariants of a group in an affine ring
• 𝑆𝐿_{𝑛}-character varieties as spaces of graphs
• The Algebra of Invariants of 3 × 3 Matrices Over a Field of Arbitrary Characteristic
• On a minimal set of generators for the invariants of 3 × 3 matrices
• The Hilbert series of rings of matrix concomitants
• Generators and relations of invariants of 2 × 2 matrices
• Relatively Free Algebras with the Identityx³ = 0^#
• The structure of the invariant ring of two matrices of degree 3
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