Involutions for upper triangular matrix algebras.

DOI10.1016/j.aam.2005.07.004zbMath1116.16029OpenAlexW2008314936MaRDI QIDQ867916

Plamen Koshlukov, Roberto La Scala, Onofrio Mario di Vincenzo

Publication date: 19 February 2007

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aam.2005.07.004

zbMATH Keywords

involutionsbases of identitiesupper triangular matricescodimensionscocharactersidentities with involutionHilbert series of free algebras

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Endomorphism rings; matrix rings (16S50) Growth rate, Gelfand-Kirillov dimension (16P90) Other kinds of identities (generalized polynomial, rational, involution) (16R50) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) Algebraic systems of matrices (15A30)

Related Items

Graded polynomial identities for the Lie algebra of upper triangular matrices of order 3 ⋮ Involutions of the second kind for upper triangular matrix algebras ⋮ Lie identities and images of Lie polynomials for the skew-symmetric elements of UT_m ⋮ Homogeneous involutions on upper triangular matrices ⋮ Graded polynomial identities as identities of universal algebras ⋮ Graded linear maps on superalgebras ⋮ Identities with involution for \(2\times 2\) upper triangular matrices algebra over a finite field ⋮ Real elements in T_n(K) ⋮ Graded polynomial identities for matrices with the transpose involution over an infinite field ⋮ Degree-inverting involution on full square and triangular matrices ⋮ Symmetric and skew-symmetric polynomial identities with involution for the upper triangular matrix algebras of even order ⋮ On the *-polynomial identities of \(M_{1,1}(E)\). ⋮ Involutions of the second kind on finitary incidence algebras ⋮ Polynomial identities in matrix algebras with pseudoinvolution ⋮ Involutions in algebras of upper-triangular matrices ⋮ Group gradings on the Lie and Jordan algebras of upper triangular matrices ⋮ Generalized quasi-Baer *-rings and Banach *-algebras ⋮ Graded identities with involution for the algebra of upper triangular matrices ⋮ Values of multilinear graded \(\ast\)-polynomials on upper triangular matrices of small dimension ⋮ Identities with involutions on incidence algebras ⋮ Superinvolutions on upper-triangular matrix algebras ⋮ Elementary gradings on the Lie algebra \(UT_n^{(-)}\) ⋮ Minimal algebras with respect to their *-exponent. ⋮ Degree-inverting involutions on matrix algebras ⋮ Involutive triangular matrix algebras ⋮ Distinguishing simple algebras by means of polynomial identities ⋮ Graded Involutions on Upper-triangular Matrix Algebras ⋮ Central polynomials with involution for the algebra of 2 × 2 upper triangular matrices ⋮ Lvov-Kaplansky conjecture on UT_m^+ with the transpose involution ⋮ Classification of Involutions on Incidence Algebras ⋮ Polynomial growth and identities of superalgebras and star-algebras. ⋮ Anti-isomorphisms and involutions on the idealization of the incidence space over the finitary incidence algebra ⋮ Automorphisms and involutions on incidence algebras ⋮ Graded involutions on block-triangular matrix algebras ⋮ Involutions in triangular groups ⋮ Anti-automorphisms and involutions on (finitary) incidence algebras

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A note on algebra automorphisms of triangular matrices over commutative rings
• Wreath products and P.I. algebras
• On codimension growth of finitely generated associative algebras
• Exponential codimension growth of PI algebras: an exact estimate
• Commutativity preserving linear maps and Lie automorphisms of triangular matrix algebras
• Abelian gradings on upper-triangular matrices
• Identities with involution for the matrix algebra of order two in characteristic \(p\).
• Gradings on the algebra of upper triangular matrices and their graded identities.
• Cocharacters, Codimensions and Hilbert Series of the Polynomial Identities for 2 × 2 Matrices with Involution
• GRADED IDENTITIES FOR THE ALGEBRA OF n×n UPPER TRIANGULAR MATRICES OVER AN INFINITE FIELD