Polynomial identities for the Jordan algebra of upper triangular matrices of order 2

DOI10.1016/j.jpaa.2012.03.009zbMath1287.17053OpenAlexW1987736610MaRDI QIDQ1936121

Fabrizio Martino, Plamen Koshlukov

Publication date: 21 February 2013

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jpaa.2012.03.009

zbMATH Keywords

Jordan algebrasupper triangular matricespolynomial identitycodimension growth

Mathematics Subject Classification ID

(T)-ideals, identities, varieties of associative rings and algebras (16R10) Rings with polynomial identity (16R99) Identities and free Jordan structures (17C05)

Related Items (18)

Graded polynomial identities for the Lie algebra of upper triangular matrices of order 3 ⋮ Group gradings on the Jordan algebra of upper triangular matrices ⋮ Graded polynomial identities for the upper triangular matrix algebra over a finite field ⋮ Varieties of special Jordan algebras of almost polynomial growth ⋮ Images of multilinear graded polynomials on upper triangular matrix algebras ⋮ Jordan algebras of a degenerate bilinear form: Specht property and their identities ⋮ Group gradings on the Lie and Jordan algebras of upper triangular matrices ⋮ Specht property of varieties of graded Lie algebras ⋮ A Lie algebra over a finite field of characteristic 2: graded polynomial identities and Specht property ⋮ The isomorphism problem in the context of PI-theory for two-dimensional Jordan algebras ⋮ Polynomial identities for the Jordan algebra of a degenerate symmetric bilinear form ⋮ A note on cocharacter sequence of Jordan upper triangular matrix algebra ⋮ Ordinary and graded cocharacter of the Jordan algebra of \(2 \times 2\) upper triangular matrices ⋮ Elementary gradings on the Lie algebra \(UT_n^{(-)}\) ⋮ Group gradings on the Lie algebra of upper triangular matrices ⋮ Specht property for some varieties of Jordan algebras of almost polynomial growth ⋮ The algebra of \(2 \times 2\) upper triangular matrices as a commutative algebra: gradings, graded polynomial identities and Specht property ⋮ Polynomial identities for the Jordan algebra of \(2 \times 2\) upper triangular matrices

Cites Work

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• Identities of the tensor square of a Grassmann algebra
• The Specht property of the ideals of identities of certain simple nonassociative algebras
• Polynomial identities for the Jordan algebra of a symmetric bilinear form
• Special varieties of Jordan algebras
• A basis for the identities of the algebra of second-order matrices over a finite field
• On codimension growth of finitely generated associative algebras
• Exponential codimension growth of PI algebras: an exact estimate
• Asymptotics for the standard and the Capelli identities.
• A finite basis for polynomial identities of the Jordan algebra of a bilinear form
• GRADED POLYNOMIAL IDENTITIES FOR THE LIE ALGEBRA sl₂(K)
• The Polynomial Identities of the Grassman Algebra
• Basis of the identities of the matrix algebra of order two over a field of characteristic \(p\neq 2\)

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