The Algebra of Invariants of 3 × 3 Matrices Over a Field of Arbitrary Characteristic

DOI10.1081/AGB-120037420zbMath1076.16020arXivmath/0606486MaRDI QIDQ3158250

Artem A. Lopatin

Publication date: 21 January 2005

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

Full work available at URL: https://arxiv.org/abs/math/0606486

zbMATH Keywords

Cayley-Hamilton theoremtrace identitiesalgebras of invariantsmatrix invariantsnilpotency degrees

Mathematics Subject Classification ID

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) (T)-ideals, identities, varieties of associative rings and algebras (16R10)

Related Items (12)

Relations between \(O(n)\)-invariants of several matrices. ⋮ Minimal generating and separating sets for O(3)-invariants of several matrices ⋮ On the nilpotency degree of the algebra with identity \(x^n=0\). ⋮ Separating invariants of three nilpotent \(3\times 3\) matrices ⋮ Relatively Free Algebras with the Identityx³ = 0^# ⋮ Minimal system of generators for O(4)-invariants of two skew-symmetric matrices ⋮ ASSOCIATIVE NIL-ALGEBRAS OVER FINITE FIELDS ⋮ Minimal affine coordinates for SL\((3,\mathbb C)\) character varieties of free groups ⋮ Orthogonal invariants of skew-symmetric matrices ⋮ Indecomposable Invariants of Quivers for Dimension (2,…,2) and Maximal Paths ⋮ On minimal generating systems for matrixO(3)-invariants ⋮ Indecomposable orthogonal invariants of several matrices over a field of positive characteristic

Cites Work

• Invariants of several matrices
• The invariant theory of \(n\times n\) matrices
• An algorithm for computing graded algebras
• Rings of matrix invariants in positive characteristic
• On the characteristic polynomial of a sum of matrices
• Endomorphisms of tensor products of exterior powers and procesi hypothesis
• Invariant functions on matrices

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