Basis of the identities of the matrix algebra of order two over a field of characteristic \(p\neq 2\)

DOI10.1006/JABR.2000.8738zbMath0988.16015OpenAlexW2050291985MaRDI QIDQ5946424

Plamen Koshlukov

Publication date: 10 April 2002

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

Full work available at URL: https://doi.org/10.1006/jabr.2000.8738

zbMATH Keywords

algebras with polynomial identitiesbases of identitiespolynomial identities of matricesstandard identities

Mathematics Subject Classification ID

Trace rings and invariant theory (associative rings and algebras) (16R30) (T)-ideals, identities, varieties of associative rings and algebras (16R10)

Related Items (34)

Tensor product theorems in positive characteristic. ⋮ -graded identities of the Lie algebras in characteristic 2 ⋮ On the graded identities for elementary gradings in matrix algebras over infinite fields. ⋮ Graded central polynomials for the matrix algebra of order two. ⋮ Central polynomials for \(\mathbb{Z}_2\)-graded algebras and for algebras with involution. ⋮ Automorphisms and superalgebra structures on the Grassmann algebra ⋮ Unnamed Item ⋮ On the polynomial identities of the algebra \(M_{11}(E)\). ⋮ Matrix identities with forms. ⋮ Graded monomial identities and almost non-degenerate gradings on matrices ⋮ Images of multilinear graded polynomials on upper triangular matrix algebras ⋮ Polynomial identities for the Jordan algebra of upper triangular matrices of order 2 ⋮ Codimension growth for polynomial identities of representations of Lie algebras ⋮ A Lie algebra over a finite field of characteristic 2: graded polynomial identities and Specht property ⋮ Graded identities and central polynomials for the verbally prime algebras ⋮ The isomorphism problem in the context of PI-theory for two-dimensional Jordan algebras ⋮ Asymptotics of graded codimension of upper triangular matrices ⋮ Central polynomials in the matrix algebra of order two. ⋮ GRADED POLYNOMIAL IDENTITIES FOR THE LIE ALGEBRA sl₂(K) ⋮ Ordinary and graded cocharacter of the Jordan algebra of \(2 \times 2\) upper triangular matrices ⋮ On the nilindex of the radical of a relatively free associative algebra. ⋮ Elementary gradings on the Lie algebra \(UT_n^{(-)}\) ⋮ Weak polynomial identities and their applications ⋮ \(G\)-identities for the Lie algebra \(sl_2(\mathbb{C})\) ⋮ Graded polynomial identities and central polynomials of matrices over an infinite integral domain ⋮ 2-graded polynomial identities for the Jordan algebra of the symmetric matrices of order two ⋮ Graded identities for T-prime algebras over fields of positive characteristic ⋮ Robinson–Schensted–Knuth Correspondence and Weak Polynomial Identities of M_1,1(E) ⋮ Identities with involution for the matrix algebra of order two in characteristic \(p\). ⋮ Graded identities of block-triangular matrices ⋮ Graded central polynomials for the algebra \(M_n(K)\). ⋮ Polynomial identities for the Jordan algebra of \(2 \times 2\) upper triangular matrices ⋮ Graded algebras with polynomial growth of their codimensions. ⋮ A basis for the graded identities of the matrix algebra of order two over a finite field of characteristic \(p\neq 2\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Computing with 2\(\times 2\) matrices
• A characteristic free approach to invariant theory
• A basis for the identities of the algebra of second-order matrices over a finite field
• Weak polynomial identities for the matrix algebra of order two
• Finite basing of the identities of a matrix algebra of second order over a field of characteristic zero
• Generic \(2\times 2\) matrices in positive characteristic
• Gesetze in Ringen. I
• On the Foundations of Combinatorial Theory: IX Combinatorial Methods in Invariant Theory
• Abelian-By-Nilpotent Varities of Lie Algebras
• Finitely based ideals of weak polynomial identities
• Identities of representations of nilpotent lie algebras
• Ideals of identities of representations of nilpotent lie algebras
• VARIETIES OF LIE ALGEBRAS
• On the identities of the Grassmann algebras in characteristic \(p>0\)

This page was built for publication: Basis of the identities of the matrix algebra of order two over a field of characteristic \(p\neq 2\)