Cayley's hyperdeterminant: A combinatorial approach via representation theory

DOI10.1016/j.laa.2012.01.037zbMath1270.15016arXiv1106.5068OpenAlexW1974126243MaRDI QIDQ417565

Mohsen Soltanifar, Mikelis G. Bickis, Murray R. Bremner

Publication date: 14 May 2012

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1106.5068

zbMATH Keywords

representation theorypolynomial invariantsCayley hyperdeterminantmultidimensional matrices

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Determinants, permanents, traces, other special matrix functions (15A15) Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Vector and tensor algebra, theory of invariants (15A72) Actions of groups on commutative rings; invariant theory (13A50) Contingency tables (62H17)

Related Items (5)

Fundamental invariants for the action of $SL_3(\mathbb {C}) \times SL_3(\mathbb {C}) \times SL_3(\mathbb {C})$ on $3 \times 3 \times 3$ arrays ⋮ Rank classification of tensors over ⋮ Unnamed Item ⋮ The maximum rank of 2 × ⋯ × 2 tensors over 𝔽₂ ⋮ Canonical forms of 2 × 2 × 2 and 2 × 2 × 2 × 2 arrays over 𝔽₂and 𝔽₃

Cites Work

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• Tensor Decompositions and Applications
• Brunn--Minkowski inequalities for contingency tables and integer flows
• A geometric approach to the Kronecker problem. I: The two row case.
• Kruskal's polynomial for \(2 \times{}2 \times{}2\) arrays and a generalization to \(2 \times{}n \times{}n\) arrays
• Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics
• Hyperdeterminants
• Binary cumulant varieties
• Phylogenetic invariants for stationary base composition
• Lie groups. An approach through invariants and representations
• The rank of a 2 × 2 × 2 tensor
• Tensor rank is NP-complete
• Algebraic invariants of five qubits
• The hyperdeterminant and triangulations of the 4-cube
• On polynomial invariants of several qubits
• Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem
• Irreducible finite-dimensional representations of equivariant map algebras
• Naive Lie Theory
• Introduction to Lie Algebras and Representation Theory
• Subtracting a best rank-1 approximation may increase tensor rank

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