DEFINING RELATIONS OF LOW DEGREE OF INVARIANTS OF TWO 4 × 4 MATRICES

DOI10.1142/S0218196709004981zbMath1181.16021arXiv0708.3583OpenAlexW2042474728MaRDI QIDQ3621433

Roberto La Scala, Vesselin Drensky

Publication date: 21 April 2009

Published in: International Journal of Algebra and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0708.3583

zbMATH Keywords

defining relationsmatrix invariantsgeneric matricestrace algebrasminimal generating systemsgenerating sets of invariantsrelations among invariants

Mathematics Subject Classification ID

Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) (16S15) Vector and tensor algebra, theory of invariants (15A72) Actions of groups on commutative rings; invariant theory (13A50) Trace rings and invariant theory (associative rings and algebras) (16R30)

Related Items (3)

Generating sets for coordinate rings of character varieties ⋮ Invariants of pairs in 𝑆𝐿(4,ℂ) and 𝕊𝕌(3,1) ⋮ Defining relations of minimal degree of the trace algebra of \(3\times 3\) matrices.

Cites Work

• Poincaré series of some pure and mixed trace algebras of two generic matrices.
• Hilbert series of fixed free algebras and noncommutative classical invariant theory
• Young diagrams and determinantal varieties
• The invariant theory of \(n\times n\) matrices
• Denominators for the Poincaré series of invariants of small matrices
• Defining relations of invariants of two \(3\times 3\) matrices.
• Polynomial identities for a family of simple jordan algebras
• On a minimal set of generators for the invariants of 3 × 3 matrices
• The ring of invariants of matrices
• The structure of the invariant ring of two matrices of degree 3
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