Computing with 2$\times 2$ matrices

DOI10.1016/0021-8693(84)90141-8zbMath0537.16013OpenAlexW2061918313MaRDI QIDQ792420

Publication date: 1984

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

Full work available at URL: https://doi.org/10.1016/0021-8693(84)90141-8

zbMATH Keywords

centres algebra of matrices traces Young diagrams linear bases generic matrices graded vector spaces Poincare series

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Representations of finite symmetric groups (20C30) Vector and tensor algebra, theory of invariants (15A72) Rings with polynomial identity (16Rxx)

Related Items (50)

Generic $2\times 2$ matrices with involution ⋮ Matrix invariants over an infinite field of finite characteristic ⋮ Asymptotics and algebraicity of some generating functions ⋮ Generators and relations of invariants of 2 × 2 matrices ⋮ Proj of generic matrices and trace rings ⋮ Character algebras of decorated $SL_{2}(\mathbb C)$-local systems ⋮ Matrix invariants and complete intersections ⋮ Regularity of trace rings of generic matrices ⋮ Explicit codimension formulas of certain T-ideals ⋮ Algebraic properties of codimension series of PI-algebras. ⋮ On $*$-cocharacters of $M_{1,1}(E)$. ⋮ Growth for algebras satisfying polynomial identities. ⋮ Bound for the cocharacters of the identities of irreducible representations of $\mathfrak{sl}_2(\mathbb{C})$ ⋮ Multiplicities of Schur functions in invariants of two $3\times 3$ matrices ⋮ Sign trace identities ⋮ A combinatorial proof for an identity of procesi ofS_ncharacters ⋮ A quantum-trace determinantal formula for matrix commutators, and applications ⋮ On the growth of graded polynomial identities of ⋮ Separating invariants of three nilpotent $3\times 3$ matrices ⋮ Generic $2\times 2$ matrices in positive characteristic ⋮ An $L_2$-quotient algorithm for finitely presented groups on arbitrarily many generators. ⋮ Lie automorphisms of the algebra of two generic $2\times 2$ matrices ⋮ Relatively Free Algebras with the Identityx³ = 0^# ⋮ Minimal system of generators for O(4)-invariants of two skew-symmetric matrices ⋮ Growth in SL2 over finite fields ⋮ Computable identities in the algebra of formal matrices ⋮ The Hilbert series of rings of matrix concomitants ⋮ Approximate values of the multiplicities in the arm of the cocharacter sequence of $M_{2,1}$. ⋮ Cocharacters for the weak polynomial identities of the Lie algebra of $3 \times 3$ skew-symmetric matrices ⋮ Computing the ℤ₂-Cocharacter of 3 × 3 Matrices of Odd Degree ⋮ Orthogonal invariants of skew-symmetric matrices ⋮ $*$-polynomial identities of a nonsymmetric $*$-minimal algebra. ⋮ Basis of the identities of the matrix algebra of order two over a field of characteristic $p\neq 2$ ⋮ Explicit descriptions of trace rings of generic 2 by 2 matrices ⋮ Indecomposable Invariants of Quivers for Dimension (2,…,2) and Maximal Paths ⋮ Separating invariants for $2 \times 2$ matrices ⋮ Asymptotics for the multiplicities in the cocharacters of some PI-algebras ⋮ On minimal generating systems for matrixO(3)-invariants ⋮ Varieties of pro-$p$-groups of second order matrices ⋮ Polynomial identities for 2$\times 2$ matrices ⋮ MULTIPLICITIES IN THE MIXED TRACE COCHARACTER SEQUENCE OF TWO 3 × 3 MATRICES ⋮ Regev's conjecture and codimensions of P.I. algebras. ⋮ New polynomial identities for $2\times 2$ generic matrices in characteristic $2$ ⋮ Indecomposable orthogonal invariants of several matrices over a field of positive characteristic ⋮ Codimensions and trace codimensions of matrices are asymptotically equal ⋮ Graded polynomial identities of matrices ⋮ Rings of matrix invariants in positive characteristic ⋮ The functional equation for Poincaré series of trace rings of generic 2$\times 2$ matrices ⋮ Trace cocharacters and the Kronecker products of Schur functions ⋮ Cocharacters of polynomial identities of block triangular matrices

Cites Work

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Computing with 2\(\times 2\) matrices